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BLAW-KNOX  TRANSMISSION  POLE 

(Patents  Applied  For) 


FOMM     NO       941 


TRANSMISSION 
TOWERS 


Being  a  reprint  of  a  paper  read 
by  E.  L.  Gemmill,  Chief  Engi- 
neer of  the  Transmission  Tower 
Department  of  Blaw-Knox 
Company,  Pittsburgh,  before  the 
Engineering  Society  of  the  same 
company. 

To  which  have  been  added 
many  tables  of  properties  of 
wires,  sags,  loads  and  curves, 
formulae,  etc.,  to  make  it  a  most 
complete  reference  book  for  all 
interested  in  the  subject. 


BLAW-KNOX  COMPANY 

GENERAL  OFFICES:  PITTSBURGH,  PA. 

DISTRICT  OFFICES 

NEW  YORK  CHICAGO  SAN  FRANCISCO 

165  Broadway  Peoples  Gas  Bldg.  Monadnock  Bldg. 

BOSTON  DETROIT 

Little  Bldg.  Lincoln  Bldg. 


Catalog  No.  20 — Copyright  1920,  Blaw-Knox  Company 


Fig.  A— Double  Circuit  Tower,  for  110,000  Volt  Line 


TRANSMISSION  LINE 
TOWERS 

It  is  only  within  the  last  twenty-five  to  thirty  years  that  it  has  been 
considered  advisable  to  carry  overhead  electric  power  transmission 
lines  on  anything  else  than  wood  poles.  But  with  the  ever  increasing 
tendency  to  concentrate  power  house  units,  and  consequently  to  make 
fewer  and  larger  installations,  spaced  farther  apart,  it  has  become 
necessary  to  transmit  electrical  energy  over  greater  distances.  This, 
in  turn,  has  made  it  advisable  to  set  a  higher  limit  for  the  voltage  at 
which  the  electrical  energy  will  be  conveyed  from  one  point  to  another, 
in  order  to  reduce  to  the  lowest  possible  minimum  the  loss  in  transmis- 
sion. The  using  of  these  higher  voltages  has,  of  course,  brought  in  its 
train  the  necessity  of  making  more  careful  provisions  for  supporting 
the  conductors  by  means  of  which  the  electrical  energy  is  transmitted 
from  one  point  to  another.  Naturally,  the  first  change  made  in  the 
general  scheme  in  vogue  was  to  place  the  conductors  farther  apart, 
which  necessitated  the  use  of  better  cross  arms  for  supporting  them. 
At  the  same  time  it  was  also  imperative  that,  with  increased  voltage, 
more  clearance  be  allowed  between  the  ground  and  the  lowest  conduc- 
tor wires  under  the  worst  possible  conditions  of  operation.  This 
could  best  be  accomplished  by  making  the  supporting  structures 
higher. 

So  long  as  the  wires  were  kept  only  a  short  distance  above  the 
ground,  the  wood  poles  made  an  ideal  support  for  them  under  ordinary 
conditions;  but  when  higher  supports  had  to  be  considered,  transmis- 
sion line  engineers  began  looking  about  for  other  supporting  structures 
which  would  lend  themselves  more  readily  to  all  the  varying  condi- 
tions of  service. 

The  steel  structure  was  immediately  suggested  as  the  proper  support 
to  take  the  place  of  the  wood  poles,  and  many  arguments  were  ad- 
vanced in  its  favor. 

But  these  supports  when  built  of  steel  were  more  expensive  than  the 
wood  poles  had  been,  and  in  order  to  keep  the  total  cost  of  the  line 
equipment  down  to  a  minimum,  and  to  make  such  an  installation  com- 
pare favorably  with  a  similar  line  using  the  wood  poles,  it  became 
necessary  to  space  the  steel  supports  farther  apart,  so  as  to  use  fewer 
of  them  to  cover  the  same  length  of  line. 


4fl44<)9 


4  Transmission  Towers 

The  steel  support,  however,  had  come  to  stay,  and  the  whole  prob- 
lem resolved  itself  into  a  matter  of  making  a  careful  investigation  and 
study  of  each  installation,  in  order  that  there  might  be  used  that  sys- 
tem which  apparently  worked  out  the  best  in  each  particular  case. 
From  these  several  projects  there  have  been  evolved  the  different 
types  of  structures  in  use  today  for  transmission  line  work.  They 
may  be  roughly  divided  into  three  general  types,  namely: 

Poles 

Flexible  Frames 

Rigid  Towers 
POLES 

All  supports  that  are  relatively  small  at  the  base  or  ground  line  are 
generally  classified  as  Poles.  In  plan  at  both  ground  line  and  near  the 
top  they  are  made  in  several  different  shapes.  They  may  be  round, 
square,  rectangular,  triangular,  or  of  almost  any  other  section.  As  a 
rule,  their  general  outline  is  continued  below  the  ground  line  to  the 
extreme  bottom  of  the  anchorage.  They  are  usually  intended  merely 
to  take  care  of  the  vertical  loads  combined  with  horizontal  loads 
across  or  at  right  angles  to  the  direction  of  the  line.  They  may  have 
greater  strength  transverse  to  the  line  than  in  the  direction  of  the  line, 
but  they  are  often  made  of  the  same  strength  in  each  direction.  Poles 
are  very  rarely  designed  to  take  care  of  any  load  in  the  direction  of  the 
line  when  combined  with  the  specified  load  across  the  line.  They 
must  be  spaced  closer  together  than  the  heavier  structures  but  can  be 
spaced  much  farther  apart  than  wood  poles.  A  very  common  spacing 
for  steel  poles  is  about  300  feet  apart. 

FLEXIBLE  FRAMES 

Flexible  Frames  are  heavier  structures  than  the  poles,  and  are 
intended  to  take  care  of  longer  spans.  Like  the  poles,  their  chief  func- 
tion is  to  take  care  primarily  of  transverse  loads  with  a  small  margin  of 
safety  so  that  under  unusual  conditions  of  service  they  could  also  pro- 
vide a  little  resistance  in  the  direction  of  the  line;  i.  e.,  in  a  measure, 
distribute  a  load  coming  in  this  direction  over  a  number  of  supporting 
structures,  and  transfer  such  a  load  to  the  still  heavier  structures 
placed  at  regular  intervals  in  the  line.  Or  the  flexible  frames  may 
transfer  all  loads  coming  on  them  in  the  direction  of  the  line  to  a  point 
where  they  will  be  resisted,  by  a  frame  of  similar  construction  and 


Transmission  Towers  5 

strength,  but  which  is  made  secure  against  the  action  of  such  loads  by 
being  anchored  in  this  direction  with  guy  lines. 

These  flexible  frames  are  almost  always  rectangular  in  plan.  Gener- 
ally, the  parallel  faces  in  both  directions  will  get  smaller  as  the  top  is 
approached,  but  often  the  two  faces  parallel  to  the  direction  of  the  line 
will  be  of  the  same  width  from  the  bottom  to  the  top.  But  the  two 
faces  transverse  to  the  line  almost  always  taper  from  the  ground  line 
up,  and  get  smaller  toward  the  top.  The  two  faces  parallel  to  the  line 
are  generally  extended  below  the  ground  line  to  form  the  anchorages. 

RIGID  TOWERS 

Rigid  Towers  are  the  largest  and  heaviest  structures  made  for 
transmission  line  supports,  and,  as  would  be  implied  by  the  designa- 
tion given  them,  they  are  intended  to  have  strength  to  carry  loads 
coming  upon  them,  either  in  the  direction  of  the  line  or  at  right  angles 
to  this  direction.  They  are  usually  designed  to  take  a  combination  of 
loads  in  both  directions.  These  towers  are  built  in  triangular,  rec- 
tangular, and  square  types,  depending  upon  the  particular  conditions 
under  which  the  structure  is  to  be  used.  When  a  plan  of  the  tower  at 
the  ground  line  is  square  in  outline,  each  side  of  the  square  will  be  very 
much  larger  than  in  the  case  of  either  poles  or  flexible  frames.  The 
width  of  one  side  of  a  rigid  tower,  measured  at  the  ground  line,  will 
vary  somewhere  between  about  one-seventh  and  one-third  of  the  total 
height  of  the  structure.  This  dimension  is  usually  determined  by  the 
construction  which  will  give  the  most  economical  design,  especially 
when  there  are  a  large  number  of  the  towers  required;  but  it  often 
happens  that  the  outline  of  one  or  more  of  the  structures  will  be  deter- 
mined by  local  conditions  which  are  entirely  foreign  to  the  matter  of 
economy  of  design.  Then,  too,  the  conditions  of  loading  may  be  such 
as  to  make  a  special  outline  the  most  economical  design. 

LOADINGS 

There  are  three  kinds  of  loads  which  come  upon  transmission  line 
supports: 

(1)  The  dead  load  of  the  wires  together  with  any  coating  on 

them;  also  the  dead  weight  of  the  structure  itself. 

(2)  Wind  loads  on  the  wires  and  the  structure  transverse  to 

the  direction  of  the  line. 


6  Transmission  Towers 

(3)  Pulls  in  the  direction  of  the  line  caused  by  the  dead  load 
and  the  wind  load  on  the  wires. 

The  dead  load  on  the  wires  consists  of  the  weight  of  the  wire  itself, 
plus  the  weight  of  any  insulating  covering,  plus  the  weight  of  any  coat- 
ing of  snow  or  sleet.  In  most  installations  the  conductors  are  not 
covered  with  any  insulating  material,  and  hence  at  the  higher  tempera- 
tures the  dead  load  will  be  the  weight  of  the  wire  only.  At  the  lower 
temperatures  the  wires  may  be  coated  with  a  layer  of  ice,  varying  up 
to  a  thickness  of  1 "  or  more,  all  around  the  wire.  In  some  instances 
ice  has  been  known  to  accumulate  on  conductor  wires  until  the  thick- 
ness of  the  layer  would  be  as  much  as  1}^"  all  around  the  wire.  But 
such  instances  are  very  rare,  especially  on  wires  carrying  high  voltages 
because  there  is  generally  enough  heat  in  these  wires  to  interfere  with 
the  accumulation  of  much  ice  on  them.  But  the  heaviest  coating  of 
ice  alone  does  not  often  produce  the  worst  conditions  of  loading  for 
the  conductor  and  the  supporting  structure.  The  worst  condition  of 
loading  is  that  resulting  from  the  strongest  wind  blowing  against  a 
conductor  covered  with  that  coating  which  offers  the  greatest  area  of 
exposed  surface  to  the  direction  of  the  wind  under  all  the  several  con- 
ditions obtaining.  This  will  almost  always  be  true  when  the  wind  is 
blowing  horizontally  and  at  right  angles  to  the  direction  of  the  line. 
In  this  case  the  total  horizontal  load  on  the  supporting  structure  from 
the  wires  is  the  combination  of  the  wind  load  against  the  wires  and  the 
unbalanced  pull  in  the  direction  of  the  line,  which  is  produced  by  the 
resultant  of  the  horizontal  wind  load  and  the  weight  of  the  wire  itself 
and  any  covering.  But  it  does  not  follow  that  this  condition  will 
always  give  the  maximum  load  on  the  structure.  In  mountainous 
districts  it  may  happen  that  a  transmission  line  will  be  subjected  to  a 
gust  of  wind  blowing  almost  vertically  downward,  in  which  case  this 
pressure,  being  added  directly  to  the  weight  of  the  wire  and  the  ice 
load,  may  lead  to  much  more  serious  results  than  a  wind  of  equal  or 
even  greater  intensity  blowing  horizontally  across  the  line.  It  may 
happen  in  some  districts  where  large  sleet  deposits  are  to  be  encoun- 
tered, that  the  vertical  load  from  the  dead  weight  of  the  wire  and  its 
coating  of  ice  will  be  so  great  as  to  produce  in  the  wire  a  tension  large 
enough  to  break  the  wire,  even  without  any  added  load  from  the  wind. 
This  is  especially  true  if  the  wire  is  strung  with  a  very  small  sag. 

Since  the  design  of  the  transmission  line  supports  is  determined  very 
largely  by  the  loads  which  it  is  assumed  will  come  upon  them,  and 


Transmission  Towers  7 

since  the  load  resulting  from  the  pull  in  the  direction  of  the  line  is  very 
often  the  dominating  factor;  and,  further,  since  this  load  is  a  function 
of  the  resultant  load  on  the  wire  produced  by  the  wind  load  and  the 
dead  load,  it  naturally  follows  that  the  assumptions  made  regarding  the 
amount  of  this  resultant  loading  are  a  matter  of  prime  importance. 
For  this  reason  some  very  extensive  experimenting  has  been  done  to 
determine  the  amount  of  wind  pressure  against  wires,  either  bare  or 
covered,  under  extreme  conditions  of  velocity,  density  of  air  and  tem- 
perature. Careful  observations  have  also  been  made  to  find  out,  as 
near  as  possible,  what  is  the  maximum  quantity  of  ice  that  will  adhere 
to  a  wire  during  and  after  a  heavy  storm.  It  not  infrequently  happens 
that  the  temperature  falls  and  the  wind  velocity  increases  immediately 
after  a  sleet  storm.  The  falling  temperature,  of  course,  tends  to  make 
the  ice  adhere  more  closely  to  the  wires.  On  the  other  hand,  a  rising 
wind  will  tend  to  remove  some  of  the  ice  from  the  wires. 

In  places  where  the  lower  temperatures  prevail,  the  wind  velocity 
rarely  gets  to  be  as  high  as  in  the  warmer  districts  where  sleet  cannot 
form.  On  the  other  hand,  a  moderate  wind  acting  on  a  wire  covered 
with  a  coating  of  ice,  will  oftentimes  put  much  more  stress  into  the 
wire  than  a  higher  wind  acting  on  the  bare  wire.  This  means  that  the 
conditions  of  loading  are  altogether  different  for  different  sections  of 
the  country.  It  is  now  generally  assumed  that  in  those  districts  where 
sleet  formation  is  to  be  met,  the  worst  condition  of  loading  on  the  wire 
will  be  obtained  when  the  wires  are  covered  with  a  layer  of  ice  Yl" 
thick,  the  amount  of  the  wind  pressure  on  them,  of  course,  depending 
upon  the  wind  velocity  and  the  density  of  the  air. 

WIND  PRESSURE  ON  PLANE  SURFACES 

The  wind  pressure  per  unit  area  on  a  surface  may  be  obtained  by  the 
following  formula: 

V2W 

P  =  K  — —  in  which 
2  g 

v   =  velocity  of  wind  in  feet  per  second; 
W  =  weight  of  air  per  unit  cube; 
g   =  acceleration  of  gravity  in  corresponding  units; 
K  =  coefficient  for  the  shape  of  the  surface. 

v2W 
The  factor  — —  is  called  the  velocity  head. 


8  Transmission  Towers 

In  considering  the  pressure  on  any  flat  surface  normal  to  the  direc- 
tion of  the  wind,  the  pressure  may  be  regarded  as  composed  of  two 

parts : 

(1)  Front  Pressure 

(2)  Back  Pressure 

The  front  pressure  is  greatest  at  the  center  of  the  figure,  where  its 
highest  value  is  equal  to  that  due  to  the  velocity  head.  It  decreases 
toward  the  edges.  The  following  conclusions  are  generally  regarded 
as  fair  and  reliable  deductions  from  the  results  of  many  experiments 
made  by  several  investigators,  to  determine  the  amount  and  distribu- 
tion of  wind  pressures  on  flat  surfaces : 

(1)  The  gross  front  pressure  for  a  circle  is  about  75%  of  that 

due  to  the  velocity  head,  while  for  a  square  it  is  about 
70%,  and  for  a  rectangle  whose  length  is  very  long 
compared  with  its  width  it  is  somewhere  between  83% 
and  86%. 

(2)  The  back  pressure  is  nearly  uniform  over  the  whole  area 

except  at  the  edges. 

(3)  This  back  pressure  is  dependent  on  the  perimeter  of  the 

surface  and  will  vary  between  negative  values  of  40% 
and  100%  of  the  velocity  head. 

(4)  The  maximum  total  pressure  on  an  indefinitely  long  rec- 

tangle of  measurable  width  may  be  taken  at  1.83  times 
the  velocity  head  pressure.  For  a  very  small  square, 
the  coefficient  may  be  as  small  as  1 . 1 . 

Using  the  value  for  W  corresponding  to  a  temperature  of  freezing, 
or  32°  F.,  and  a  barometric  height  of  30  inches,  which  is  0.08071 
pounds  per  cubic  foot,  and  changing  the  wind  velocity  from  feet  per 
second  to  miles  per  hour,  the  formula  for  normal  pressure  per  square 
foot  on  a  flat  surface  of  rectangular  outline  becomes : 

P  _  i  o,  x  0-08071         5280  5280 

3  X  2  x  32.2  X  60760  X  60^60  X  V 
or  P  =  0.0049335     V2 

WIND  PRESSURE  ON  WIRES 

In  the  case  of  cylindrical  wires  the  pressure  per  square  foot  of  pro- 
jected area  is  less  than  on  flat  surfaces.  The  coefficient  by  which  the 
pressure  on  flat  surfaces  must  be  multiplied  to  obtain  the  pressure  on 


Transmission  Towers  9 

the  projected  surface  of  a  smooth  cylinder,  varies,  according  to  different 
authorities,  from  45%  to  79%.  Almost  all  Engineers  in  this  country 
assume  this  coefficient  to  be  one-half,  and,  on  this  assumption  our 
formula  becomes 

P  =  0.00246675     V2 

for  the  pressure  per  square  foot  on  the  projected  area  of  the  wire,  with 
any  coating  it  may  have  on  it. 

Mr.  H.  W.  Buck  has  given  the  results  of  a  series  of  wind  pressure 
experiments  made  at  Niagara  on  a  950  ft.  span  of  .58  inch  stranded 
cable,  erected  so  as  to  be  normal  to  the  usual  wind.  From  the  data 
obtained,  the  following  formula  was  derived: 

P  =  0.0025  V2 
in  which 

P  =  Pressure  in  pounds  per  sq.  ft.  of  projected  area 
V  =  Wind  velocity  in  miles  per  hour. 

For  solid  wire  previous  experimenters  had  derived  the  formula 

P  =  0.002  V2 

It  is  to  be  noted  that  Mr.  Buck's  formula  gives  values  for  pressures 
25%  in  excess  of  the  other  formulas,  which  might  be  attributed  to  the 
fact  that  for  a  given  diameter,  a  cable  made  up  of  several  strands,  pre-t 
sents  for  wind  pressure  a  different  kind  of  surface  than  a  single  wire. 
If  we  could  be  sure  that  this  difference  exists,  then  it  would  be  well 
worth  while  to  take  this  into  consideration  when  determining  the  loads 
for  which  a  tower  is  to  be  designed,  and  to  make  a  careful  distinction 
between  towers  which  are  to  support  solid  wires  and  those  which  are  to 
carry  stranded  cables.  Almost  all  Engineers  are  inclined  to  accept  the 
formula  given  by  Mr.  Buck,  and  to  assume  it  to  be  correct  for  both 
types  of  conductors.  The  fact  that  this  formula  agrees  so  closely  with 
the  formula  arrived  at  by  assuming  that  the  pressure  on  the  projected 
area  of  a  cylindrical  surface  is  50%  of  the  pressure  on  a  rectangular 
flat  surface,  would  seem  to  warrant  accepting  it  as  being  correct. 

WIND  VELOCITY 

In  assuming  the  loadings  for  which  a  line  of  towers  are  to  be  designed, 
the  first  thing  to  be  determined  is  the  probable  wind  velocity  which 
will  be  encountered  under  the  worst  conditions.  Our  calculations,  of 
course,  should  be  based  on  actual  velocities.  This  is  mentioned  be- 
cause it  is  necessary  to  distinguish  between  indicated  and  true  wind 


10  Transmission  Towers 

velocities.  The  indicated  velocities  are  those  determined  by  the 
United  States  Weather  Bureau.  Their  observations  are  made  with 
the  cup  anemometer  and  are  taken  over  five  minute  intervals.  The 
wind  velocities  over  these  short  periods  of  time  are  calculated  on  the 
assumption  that  the  velocity  of  the  cups  is  one-third  of  the  true  velo- 
city of  the  wind,  for  both  great  and  small  velocities  alike.  As  the  result 
of  considerable  investigation,  it  has  been  found  that  this  assumption 
is  not  correct,  but  that  the  indicated  velocity  must  be  corrected  by  a 
logarithmic  factor,  to  convert  it  into  the  true  velocity.  The  actual 
wind  velocities  corresponding  to  definite  indicated  velocities,  as  given 
by  the  United  States  Weather  Reports,  are  as  follows : 

Indicated  Actual  Indicated  Actual 

10  9.6  60  48.0 

20  17.8  70  55.2 

30  25.7  .     80  62.2 

40  33.3  90  69.2 

50  40.8  100  76.2 

It  is  generally  conceded  that  the  wind  pressure  increases  with  the 
height  above  the  ground,  and  that  it  is  more  severe  in  exposed  posi- 
tions, and  where  the  line  runs  through  wide  stretches  of  open  country, 
than  it  is  in  places  which  are  more  or  less  protected  by  their  sur- 
roundings. 

If  we  accept  the  theory  advanced  by  some,  to  the  effect  that  the 
ground  surface  offers  a  resistance  to  the  wind,  which  materially  lessens 
its  force,  then  we  must  conclude  that  after  a  certain  altitude  has  been 
reached  the  effect  of  this  resistance  becomes  negligible,  and  that 
beyond  that  altitude  the  rate  of  increase  in  wind  pressure  must  be 
small.  This  is  especially  true,  because  the  density  of  the  air  is  less  in 
the  higher  altitudes,  which  tends  to  counteract  some  of  the  effect  of 
increases  in  velocity.  But  experimental  data  bearing  on  this  matter 
are  very  limited,  so  that  the  rate  of  increase  in  wind  pressures  for  higher 
elevations  above  the  ground,  must  in  each  case  be  determined  by  the 
judgment  of  the  Engineer  who  is  designing  the  installation. 

The  curve  on  Fig.  1  shows  the  relationship  between  Indicated 
velocity  and  Actual  velocity,  and  the  curve  on  Fig.,  2  shows  the  pres- 
sure in  pounds  per  square  foot  of  projected  area  of  wire,  corresponding 
to  actual  velocities  in  miles  per  hour.  By  placing  above  the  curve 
given  on  Fig.  2  a  similar  curve  corresponding  to  the  indicated  velocities, 
a  direct  comparison  between  the  two  different  velocities  may  be  made 
in  terms  of  pressure.  This  is  shown  in  Fig.  3. 


Transmission  Towers 


11 


For  the  general  run  of  transmission  line  work  no  special  allowance  is 
made  for  the  pressures  on  towers  at  different  elevations;  but  pressures 
are  used  which  are  considered  to  be  fair  average  values  for  the  par- 
ticular location  of  the  line  and  for  towers  of  heights  which  usually 
prevail.  But,  of  course,  there  is  a  distinction  made  between  require- 
ments for  a  low  pole  line  and  for  a  line  on  high  steel  towers.  This 
applies  both  to  the  wind  pressures,  which  it  is  assumed  will  be  en- 
countered, and  also  to  the  factor  of  safety  expected  in  the  construction 
throughout. 


ou 

7D 

J 

A 

fin 

V 

..    t- 

-  1- 

[ 

J 

y^ 

r 

f 

. 

f 

-  -  ? 

k 

5 
£ 

( 

A 

| 

VELOCITY, 

$  i 

^    _ 

:f             ....               ... 

I 

..              j-       - 

ACTUAL 

I  i 

.-.L. 

-  -f 

'i  ~~~~   \  — 

f 

WN  OF 

w  ACTUAL 

i 

OJ 

j 

• 

/ND/  GATED  * 

in 

WIND    VELOCITIES 

.  .7-  - 

m             -        2  -  -   -- 

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I    - 

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I 

1 

\      I 

*i       ^        fin       At 

7           K 

9          fit 

i       a 

9          IOL 

h'll 

j 

in         ?n 

INDICATED   VELOCITY;  miles  per  hour. 

Fig.  1 


12 


Transmission  Towers 


Transmission  Towers 


13 


§       § 


14 


Transmission  Towers 


STANDARD  PRACTICE  FOR  WIND  AND  ICE  LOADS 

The  Committee  on  Overhead  Line  Construction,  appointed  by  the 
National  Electric  Light  Association  of  New  York,  assumes  an  ice 
coating  %*  thick  all  around  the  wire,  for  all  sizes  of  conductors,  and 
maximum  wind  velocities  of  50  to  60  miles  per  hour,  as  being  an  aver- 
age maximum  condition  of  loading.  This  Committee  states  that  62 
miles  per  hour  is  a  velocity  not  likely  to  be  exceeded  during  the  cold 
months. 

Three  classes  of  loading  are  considered  by  the  Joint  Committee  on 
Overhead  Crossings,  as  follows: 


Class  of 
Loading: 

Vertical  Component  of 
Load  on  Wire: 

Horizontal  Component  of  Load 
on  Wire,  or  Wind  Load 
Across  Line: 

A 
B 
C 

Dead 
Dead  +  Y2"  Ice 
Dead  +  M"  Ice 

15  Lbs.  per  Sq.  Ft. 
8  Lbs.  per  Sq.  Ft. 
11  Lbs.  per  Sq.  Ft. 

For  the  Class  "B"  Loading  the  ordinary  range  of  temperature  is 
given  as— 20°  to  120°  F. 

For  the  calculation  of  pressures  on  supporting  structures  the  require- 
ments are  13  Ibs.  per  sq.  ft.  on  the  projected  area  of  closed  or  solid 
structures,  or  on  V/%  times  the  projected  area  of  latticed  structures 
The  same  Joint  Committee  allows  a  maximum  working  stress  on  cop- 
per of  50%  of  the  ultimate  breaking  stress;  in  other  words,  the  wires 
may  be  stressed  to  a  point  very  near  to  the  elastic  limit. 

An  analysis  of  these  three  classes  of  loadings  would  seem  to  suggest 
that  Class  "A"  be  used  for  lines  in  the  extreme  Southern  part  of  the 
United  States,  and  that  Class  "B"  be  used  for  all  other  lines  in  this 
country,  unless  it  be  for  a  few  lines  which  might  be  located  in  regions 
where  especially  cold  weather  is  to  be  encountered,  along  with  very 
severe  wind  storms.  For  such  lines  Class  "C"  would  certainly  be 
ample  to  take  care  of  the  most  extreme  conditions. 

Interpreting  these  loadings  in  terms  of  wind  velocities,  class  "A" 
would  allow  for  an  indicated  wind  velocity  of  101.8  miles  per  hour,  or 
an  actual  velocity  of  77.46  miles  per  hour,  acting  against  the  bare  con- 
ductor. Class  "B"  provides  for  an  indicated  wind  velocity  of  71.96 
miles  per  hour,  or  an  actual  velocity  of  56.57  miles  per  hour,  applied 


Transmission  Towers 


15 


to  the  projected  area  of  the  wire  covered  with  a  layer  of  ice  yy  thick 
all  around.  Class  "C"  assumes  an  indicated  velocity  of  85.9  miles  per 
hour,  or  an  actual  velocity  of  66.33  miles  per  hour,  against  the  wire 
covered  all  around  with  a  layer  of  ice  %"  thick. 

It  has  been  contended  by  some  Engineers  that  sleet  does  not  deposit 
readily  on  aluminum,  owing  to  the  greasy  character  of  the  oxide  which 
forms  on  the  surface  of  aluminum  conductors,  and  that  because  of  this 
fact  the  wind  loads  acting  on  such  lines  should  not  be  taken  so  high  as 
when  copper  wires  are  used.  But  the  experience  and  observation  of 
many  other  Engineers  does  not  confirm  this  assumption. 

CURVES  ASSUMED  BY  WIRES 

When  the  wires  are  strung  from  one  structure  to  another  throughout 
the  line,  they  assume  definite  curves  between  each  two  of  the  struc- 
tures, these  several  curves,  of  course,  depending  upon  the  different 
conditions  attending  the  stringing. 

If  a  heavy  uniform  string  which  is  considered  to  be  perfectly  flexible, 
is  suspended  from  two  given  points,  A  and  B,  and  is  in  equilibrium  in  a 
vertical  plane,  the  curve  in  which  it  hangs  will  be  found  to  be  the 
common  catenary.  This  is  shown  in  Fig.  4. 


Tension,  T, 


CATENARY 


At 

i  X 

*[ 

DlRKTIHX-1                                                  I 

1 

ON-X                  N 

Fig.  4 


16  Transmission  Towers 

CATENARY 

Let  D  be  the  lowest  point  of  the  catenary,  i.  e.,  the  point  at  which  the 
tangent  is  horizontal.  Take  a  horizontal  straight  line  O  X  as  the  X 
axis,  whose  distance  from  D  we  may  afterwards  choose  at  pleasure. 
Draw  D  O  perpendicular  to  this  line,  and  let  O  be  the  origin  of  co- 
ordinates. Let  0  be  the  angle  the  tangent  at  any  point  P  makes  with 
O  X.  Let  To  and  T  be  the  tensions  at  D  and  P  respectively,  and  let 
the  arc  D  P  =  Z.  The  length  D  P  of  the  string  is  in  equilibrium 
under  three  forces,  viz:  the  tensions  T0  and  T,  acting  at  D  and  P  in 
the  directions  of  the  arrows,  and  its  weight  w  Z  acting  at  the  center  of 
gravity  G  of  the  arc  D  P. 

Resolving  horizontally  we  have 

T  cos  e  =  To  (1) 

Resolving  vertically  we  have 

T  sin  0  =  w  Z  (2) 

Dividing  equation  (2)  by  equation  (1) 

dy  w  Z 

dx  "  To  (3) 

If  the  string  is  uniform  w  is  constant,  and  it  is  then  convenient  to 
write :  To  =  w  C.  To  find  the  curve  we  must  integrate  the  differential 
equation  (3). 

We  have, 


z  dz 

/.  dy  =   ± 


/.  y  +  A  =  db 

We  must  take  the  upper  sign,  for  it  is  clear  from  (3)  that,  when  x 
and  Z  increase,  y  must  also  increase.  When  Z  =  O,  y  +  A  =  C. 
Hence,  if  the  axis  of  X  is  chosen  to  be  at  a  distance  C  below  the  lowest 
point  D  of  the  string,  we  shall  have  A  =  O.  The  equation  now 

takes  the  form, 

y2  =  Z2  +  C2  (4) 


Transmission  Towers  17 

Substituting  this  value  of  y  in  (3),  we  find, 

Cdz 

V  Z2  -f  C2  =  dx' 
where  the  radical  is  to  have  the  positive  sign.     Integrating, 

C  log  (z  +  VZ2  +  C2)  =  x  -f  B 
But  x  and  Z  vanish  together,  hence  B  =  C  log  C. 
From  this  equation  we  find, 


v  z2  +  c2  +  z  =  c  e  c 

Inverting  this  and  rationalizing  the  denominator  in  the  usual  manner, 
we  have 

V  Z2  +  C2  —  Z  =  CC~' 
Adding  and  subtracting,  we  deduce  by  (4) 


The  first  of  these  is  the  Cartesian  equation  of  the  common  catenary. 
The  straight  lines  which  have  here  been  taken  as  the  axes  of  X  and  Y 
are  called,  respectively,  the  directrix  and  the  axis  of  the  catenary. 
The  point  D  is  called  the  vertex. 
Adding  the  squares  of  (1)  and  (2),  we  have  by  help  of  (4), 

T2  =  w2  (Z2  +  C2)  =  w2y2; 

/.  T  =  w  y  (6) 

The  equations  (1)  and  (2)  give  us  two  important  properties  of  the 
curve,  viz:  (1)  the  horizontal  tension  at  every  point  of  the  curve  is 
the  same  and  equal  to  w  C;  (2)  the  vertical  tension  at  any  point  P  is 
equal  to  w  Z,  where  Z  is  the  arc  measured  from  the  lowest  point.  To 
these  we  join  a  third  result  embodied  in  (6),  viz:  (3)  the  resultant 
tension  at  any  point  is  equal  to  w  y,  where  y  is  the  ordinate  measured 
from  the  directrix. 

Referring  to  Fig.  4,  let  PN  be  the  ordinate  of  P,  then  T  =  w  PN. 
Draw  NL  perpendicular  to  the  tangent  at  P,  then  the  angle  P  N  L  =  0 
Hence, 

PL  =  PN  sin  0  =  Z  by  (2) 
N  L  =  PN  cos  o  =  C  by  (1) 


18  Transmission  Towers 

These  two  geometrical  properties  of  the  curve  may  also  be  deduced 
from  its  cartesian  equation  (5). 
By  differentiating  (3)  we  find, 

1          do         1  dz  C 


1  "          /"**  •    •        I  1   /i 


cos2#      dz        C  do        cos20  (7) 

v2 
f>  is  also  =    •=; 

We  easily  deduce  from  the  right-angled  triangle  P  N  H,  that  the 
length  of  the  normal,  viz:  PH,  between  the  curve  and  the  directrix,  is 
equal  to  the  radius  of  curvature,  viz.,  p,  at  P.  At  the  lowest  point  of 

C2 
the  curve  D,  the  radius  of  curvature,  /»,  =  —  =  C.     It  will  be  noticed 

that  these  equations  contain  only  one  undetermined  constant,  viz.,  C; 
and  when  this  is  given,  the  form  of  the  curve  is  absolutely  determined. 
Its  position  in  space  depends  on  the  positions  of  the  straight  lines 
called  its  directrix  and  axis.  This  constant  C  is  called  the  parameter  of 
the  catenary.  Two  arcs  of  catenaries  which  have  their  parameters 
equal  are  said  to  be  arcs  of  equal  catenaries. 

Since  />  cos2  0  =  C,  it  is  clear  that  C  is  large  or  small  according  as 
the  curve  is  flat  or  much  curved  near  its  vertex.  Thus,  if  the  string  is 
suspended  from  two  points  A  and  B  in  the  same  horizontal  line,  then  C 
is  very  large  or  very  small  compared  with  the  distance  between  A  and 
B,  according  as  the  string  is  tight  or  loose. 

The  relationship  between  the  quantities  y,  Z,  C,  />,  and  0  and  T 
in  the  common  catenary  may  be  easily  remembered  by  referring  to  the 
rectilineal  figure  P  L  N  H.  We  have  PN  =  y,  PL  =  Z,  NL  =  C, 
PH  =  />,  T  =  w-  PN  and  the  angles  LNP,  NPH  are  each  equal  to  0. 
Thus  the  important  relations  (1),  (2),  (3),  (4)  and  (7)  follow  from  the 
ordinary  properties  of  a  right-angled  triangle. 

The  co-ordinates  of  the  center  of  curvature  for  the  catenary  are: 


a  (abscissa)  =  x  —      Vy2  —  C2 
ft  (ordinate)  =  2y 


When  two  or  more  unequal  catenaries  have  similar  outlines  so  that 

*~^ 

the  ratio  ^ is  the  same  for  all  of  them,  the  curvature  between  the 

x 

points  D  and  P  will  also  be  the  same  for  all  these  catenaries.     From 


Transmission  Towers  19 

this  it  follows  that,  at  similar  points  on  the  different  catenaries,  the 
several  radii  of  curvature  will  vary  directly  as  the  values  of  x  for  the 
different  curves.  The  radius  of  curvature  at  the  lowest  point  D  has 
already  been  shown  to  be  equal  to  C,  the  parameter  of  the  catenary. 
Since  C  and  y  —  C  both  vary  directly  as  the  value  of  x  for  these 
unequal  but  similar  catenaries,  it  is  evident  that  y  must  also  vary  in 
the  same  manner.  It  will  be  seen  from  the  triangle  PLN,  that  when 
C  and  y  both  vary  in  the  same  manner,  LP  or  Z,  which  is  the  length  of 
the  arc  DP,  must  also  vary  in  the  same  manner. 

ELASTIC  CATENARY 

When  a  heavy  elastic  string  is  suspended  from  two  fixed  points  and 
is  in  equilibrium  in  a  vertical  plane,  its  equation  may  be  found  as 
follows  : 

Using  the  same  figure  as  for  the  inelastic  string  and  denoting  the 
unstretched  length  of  arc  D  P  by  Zi,  let  us  consider  the  equilibrium  of 
the  finite  part  D  P; 

Tcosfl  =  To    (1)    .    dy  _  _  wzi  ..  Zi  ,  , 

(2)   •'  dx  •  To     "  C 


From  these  equations  we  may  deduce  expressions  for  x  and  y  in 
terms  of  some  subsidiary  variable.  Since  Zi  =  C  tan  0  by  (3),  it  will 
be  convenient  to  choose  either  Zi  or  0  as  this  new  variable.  Adding 
the  squares  of  (1)  and  (2),  we  have, 

-P  =  W2  (C»  +  Z!2)  (4) 

Since  —  =  cos  0  and  -p   =  sin  0, 
dz  dz 

we  have  by  (1)  and  (2) 


IT  *  -  -T 


where  the  constants  of  integration  have  been  chosen  to  make 

CV 
x  =  O  and  y  =  C  +  -^- 

at  the  lowest  point  of  the  elastic  catenary.     The  axis  of  X  is  then  the 
statical  directrix. 


20  Transmission  Towers 

We  have  the  following  geometrical  properties  of  the  elastic  catenary : 


(2) 
(3) 


All  of  these  reduce  to  known  properties  of  the  common  catenary 
when  E  is  made  infinite. 

These  equations  have  value  only  from  an  academic  viewpoint. 
They  are  too  unwieldy  to  be  of  any  practical  value  in  determining  the 
properties  of  curves,  assumed  by  transmission  line  wires  under  different 
working  conditions.  These  equations  would  be  still  further  compli- 
cated, if  we  attempted  to  make  them  take  care  of  changes  resulting 
from  conditions  of  loading  due  to  different  temperatures. 

PARABOLA 

If  we  consider  the  weight  of  the  wire  to  be  uniformly  distributed 
over  its  horizontal  projection,  instead  of  along  its  length,  its  equation 
will  be  found  to  be  that  of  a  parabola. 


PARABOLA 


Fig.  5 


Transmission  Towers  21 

By  referring  to  Figure  5  ^nd  considering  the  equilibrium  of  any 
part  OP  of  the  wire,  beginning  at  the  lowest  point  O,  the  forces  acting 
on  this  part  are  seen  to  be  the  horizontal  tension  H  at  O,  the  tension  T 
along  the  tangent  at  P,  and  the  total  weight  W  of  the  wire,  OP.  As 
this  weight  is  assumed  to  be  uniformly  distributed  over  the  horizontal 
projection  OP1  =  x  of  OP, 
the  weight  is  W  =  w  x,  and  bisects  OP1. 

Resolving  the  forces  in  the  horizontal  and  vertical  directions,  we 
find  as  conditions  of  equilibrium, 

—  H  +  T  ^  =  O,       —  wx  +  T  ^  =  O, 
dz  dz 

whence,  eliminating  dz,  -p-   =77  x- 

Integrating   and   considering   that  x  =  O   when   y  =  O,    we    get 

w  2  H 

y  =  777  x2,  which  may  be  put  in  the  form  x2  =  y.     This  is  the 

2  ri  w    ' 

equation  to  a  parabola. 

If  we  substitute  -  for  x,  and  S  for  y,  in  the  equation  for  the  curve, 


//y    2H 

\2/  w 


it  becomes  (  -  )     =  S  or  w  /2  =  8  HS, 

w/2 
from  which  H  =  -r^-, 

00 

which  is  the  well  known  equation  for  determining  the  horizontal  ten- 
sion in  the  wires,  when  the  two  points  of  support  are  in  the  same  hori- 
zontal plane.  In  that  case  -  equals  one-half  of  the  span,  and  S 

equals  the  sag  or  deflection  of  the  wire  below  the  plane  of  the  supports. 

The  three  forces  H,  T,  and  W,  are  in  equilibrium;  they  must  inter- 
sect in  a  point  R  which  bisects  OP1,  and  the  force  polygon  must  be 
similar  to  the  triangle  RPP1. 

Drawing  such  a  force  diagram  K  L  M,  and  making  L  M  equal  to  W 
or  w  x,  and  MK  equal  to  H,  KL  will  be  the  value  of  T  and  equal  to 
A/H2  +  (w  x)2. 

Substituting  for  H  and  x  their  values  in  terms  of  w,  /  and  S,  this 


//W/2Y,/    1Y      /w2/4 

becomes  ^(-  )    +  (wjj   =  ^- 


+  law2/22     w/ 

^-         =  -        /2  +  16S2. 


22 


Transmission  Towers 


A  quantity  \/A2  +  a2,  when  a  is  very  small  relatively  to  A,  may  be 

a2 
approximated  by  using  A  -f  -r-r ;  hence,    an    approximation    for   the 

above  value  of  T  is, 

w/2 


w  /  /7    .    16  S2\  w  /2  c 

8sV/  +  ^rj'or'^s  +  wS- 


In  this  form  it  is  very  similar  to  the  expression  for  the  tension  in  the 
wire  at  the  insulator  supports,  derived  by  assuming  the  curve  to  be  a 
catenary.  It  will  readily  be  seen  from  the  above  that  for  very  small 
sags  in  short  spans  the  maximum  tension  at  the  insulator  supports  is 
very  little  more  than  the  tension  at  the  middle  of  the  span. 

But  it  must  be  noted  that  in  order  that  the  above  assumption  may 
be  warranted,  it  is  essential  that  the  span  considered,  be  short,  and  that 
the  length  of  wire  be  little  more  than  the  span.  This,  of  course,  means 
that  the  sag  in  the  wire  must  be  rather  small. 

?  14" 

The  equation  for  the  parabola  x2  = y  has,  for  the  coefficient 

of  y,  a  constant  which  is  equal  to  four  times  the  distance  between  the 
directrix  of  the  parabola  and  the  vertex  O,  as  shown  in  Fig.  6. 


Fig.  6 


Transmission  Towers 


23 


The  directrix  is  shown  passing  through  the  point  A,  and  is  parallel  to 
the  X  axis.  The  line  OY  is  the  axis  of  the  curve.  If  a  line  is  drawn  tan- 
gent to  the  curve  at  any  point  P,  this  tangent  will  intersect  the  Y  axis  at 
a  point  B,  such  that  the  distance  BO  will  equal  the  distance  OC,  where 
C  is  the  point  of  intersection  of  the  Y  axis  with  a  line  drawn  through 
the  point  P,  parallel  to  the  X  axis.  The  length  BC  is  the  subtangent 
and  is  equal  to  twice  the  ordinate  of  the  point  of  contact.  The  line 
PD  drawn  through  the  point  P  and  perpendicular  to  the  tangent  BP, 
will  intersect  the  Y  axis  at  point  D.  The  length  CD  is  the  subnormal 
of  the  curve,  and  is  constant  for  all  points  on  the  curve.  It  is  equal  to 
one-half  the  co-efficient  of  y  in  the  original  equation,  and  is  therefore 

TT 

equal  to  — .     The  angles  TRX  and  ORB  are  each  equal  to  the  angle 

AV 

PDC  or  e. 

Tan#  = 


R  P 


PARABOLIC  ARC  WITH  SUPPORTS  AT  DIFFERENT 
ELEVATIONS 

The  curve  in  which  a  suspended  wire  hangs,  may  be  considered  to 
extend  indefinitely  in  both  directions,  and  the  suspended  wire  may  be 
secured  to  rigid  supports  at  any  two  points,  such  as  N  and  U,  lying  on 
this  curve  (Fig.  7),  without  altering  the  tension  in  the  wire.  The  law 
of  this  parabola  is 


PARABOLA 


:2  =  Ky, 

SPAN   SUPPORTS  AT 
DIFFERENT  LEVELS 


U 


Span  measured  horizontally = 


^^  i  i   "^ 1 y 

A 


24  Transmission  Towers 

and  in  the  case  of  a  suspended  wire  the  multiplier  K  is  directly  propor- 
tional to  the  tension  H,  and  inversely  proportional  to  the  density  of 
the  conductor  material.  The  value  of  K  in  terms  of  the  horizontal 
tension  and  the  weight  of  the  conductor  has  already  been  found  to 

u    2H 

be  -  . 

w 

Let  S  =  sag  below  level  of  lower  support, 

B  =  horizontal   distance   of   lowest   point   of   wire 

from  lower  support, 

h  =  difference  in  level  of  the  two  supports, 
/  =  length  of  span  measured  horizontally, 

all  as  indicated  on  Fig.  7;  then,  by  inserting  the  required  values  in 
equation  x2  =  Ky,  the  following  equations  are  derived  therefrom: 

B2  =  K  S, 

(/  —  B)2  =  K  (S  +  h),  or,  /2  —  2/B  +  B2  =  KS  +  Kh, 
from  which  B2  on  one  side  and  its  equivalent  KS  on  the  other  side  can- 
cel out,  leaving  I2  —  2/B  =  Kh. 

Therefore, 

—  Kh        ,  B2 


2        '  K 

From  an  inspection  of  the  formula  B  =  -  —,  —  ,  it  is  seen  that  if 

2>  I 

Kh  =  /2,  the  lowest  point  of  the  wire  coincides  with  the  lower  support 
N,  while  if  Kh  is  greater  than  /2,  the  distance  B  is  negative,  and  there 
may  be  a  resultant  upward  pull  on  the  lower  insulator  N  —  a  point  to 
bear  in  mind  when  considering  an  abrupt  change  in  the  grade  of  a 
transmission  line. 

We  may  consider  the  curve  of  the  wire  between  the  two  supports  N 
and  U  as  being  made  up  of  two  distinct  parts,  NO  and  OU.  The  part 
NO  will  be  equivalent  to  one-half  of  a  curve  whose  half  span  measured 
horizontally  is  B,  and  whose  sag  is  S.  Similarly,  the  part  OU  will  be 
equivalent  to  one-half  of  a  curve  whose  half  span  measured  hori- 
zontally is  /  —  B,  and  whose  sag  is  S  -)-  h. 

It  is  possible,  and  sometimes  convenient,  to  express  the  formulas  for 
wires  suspended  from  supports  not  at  the  same  level,  in  terms  of  the 
equivalent  sag  (Se)  of  the  same  wire,  subjected  to  the  same  horizontal 
tension  when  the  horizontal  span  (/)  is  unaltered,  but  the  supports  are 
on  the  same  level. 


Transmission  Towers  25 

For  such  a  condition,  the  equation  to  the  curve  becomes 

from  which 

^  =  45; 

If  we  substitute  for  K  in  the  above  formulas,  its  equivalent  value 

K  =— , 

then  we  get  the  following  set  of  formulas,  in  which  B,  S,  /,  and  h,  are  all 
as  indicated  in  Fig.  7. 


COMPARISON  OF  CATENARY  AND  PARABOLA 

If  a  straight  line  is  drawn  through  the  point  P  and  any  other  point  K 
on  the  parabola,  shown  in  Fig.  6,  and  this  chord  KP  is  bisected  at  the 
point  M,  a  line  drawn  through  this  point  M  and  parallel  to  the  Y  axis 
will  bisect  all  other  chords  which  are  parallel  to  the  chord  KP.  From 
this  it  follows  that  a  line  SU  drawn  tangent  to  the  parabola  and 
parallel  to  the  chord  KP,  will  be  tangent  to  the  curve  at  a  point  L 
which  lies  on  a  line  that  is  drawn  parallel  to  the  Y  axis  and  through  the 
point  M.  Another  property  of  the  parabola  is,  that  the  tangents  to 
the  curve  at  the  points  K  and  P  will  intersect  at  the  point  N,  which 
also  lies  on  the  line  that  passes  through  the  points  L  and  M.  If  the 
horizontal  projection  of  the  chord  KP  be  designated  by  /,  then  the 
horizontal  projection  of  KM,  MP,  KN,  and  NP  will  each  be  equal  to 

1AL 

The  total  tension  T  in  the  wire  at  any  point  on  the  curve  equals 


+   (wx)2, 
or, 


T,.ygy+- 

But  it  is  seen  from  the  figure  that 

V(!7 


+  x2  =  DP, 
/.  T  =  w     DP  . 


26  Transmission  Towers 

In  the  case  of  the  catenary  the  total  tension  in  the  wire  is 

T  =  w  y 

in  which  

y  =  VC2  +  Z2 
But,  when  we  compare  a  catenary  and  a  parabola  having  equivalent 

TT 

horizontal  tensions.  C  =  — .it  will  be  seen  that  the  two  formulas  for 

w 

total  tension  in  the  wire  differ  only  in  that  the  value  Z,  which  is  the 
true  length  of  the  arc,  is  used  in  the  one  case,  -where  x,  which  is  the 
horizontal  projection  of  the  length,  is  used  in  the  other.  But  T  will 
always  be  greater  for  the  catenary  except  at  the  lowest  point  of  the 
curve. 

The  radius  of  curvature  of  the  parabola 

2H  ^ 

x2  = y  is  p  =      w 

w    '  c. 

SmV 

in  which  y  is  the  angle  which  the  tangent  to  the  curve  makes  with  the 
Y  axis. 

TT 

/>  sin3  <f  =  —  =  DP  sin  y,  or,  />  sin2  y  =  DP 

from  which  DP        ^ 

DZ. 


sn  <p 

TT 

If  we  substitute  C  for—,  the  radius  of  curvature  is, 

C  C 

sin3  <f>      cos3  9 
In  the  case  of  the  catenary, 


cos2  o 


A  comparison  of  these  two,  shows  that  the  radius  of  curvature  for 
the  parabola,  at  a  point  where  the  tangent  makes  an  angle  0  with  the 

horizontal,  is times  that  for  a  similar  point  on  the  catenary. 


Transmission  Towers 


27 


At  the  lowest  point  of  the  curve  the  radius  of  curvature  is  the  same  for 
both  the  parabola  and  the  catenary,  when  the  horizontal  tension  is  the 
same.  It  is  also  true  that,  when  the  horizontal  tension  at  the  lowest 
point  of  the  parabola  is  equivalent  to  that  at  the  lowest  point  of  the 
catenary  for  the  same  span  and  loading  conditions,  the  sag  at  this 
point  below  the  plane  of  the  supports  will  be  very  nearly  the  same  for 
the  two  curves. 

But  the  outlines  of  the  two  curves  differ  at  all  points  between  the 
lowest  point  and  the  point  of  support.  This  difference  between  the 
outlines  of  the  two  curves  becomes  greater  as  the  spans  and  the  sags 
are  made  larger.  It  is  because  of  this  difference  in  the  outlines  of  the 
two  curves  that  the  sags  will  be  nearly  equal  for  only  one  loading  con- 
dition. Any  change  in  the  loading  condition  will  produce  different 
changes  in  the  lengths  of  the  two  curves,  and  hence,  will  make  the  sags 
different. 

REACTIONS  FOR  SPANS  ON  INCLINES 

When  wires  are  strung  on  towers  that  are  located  on  steep  grades,  it 
is  very  necessary  that  we  determine  carefully  the  reactions  at  the 
points  of  support  and  also  the  deflection  of  the  wire  away  from  a 
straight  line  joining  the  two  points  of  support  for  any  given  span. 
This  case  is  shown  in  Fig.  8. 


PARABOLA 


Fig.  8 


28  Transmission  Towers 

If  we  have  given  the  horizontal  distance,  /,  between  the  supports  A 
and  B  and  also  the  vertical  distance,  h,  that  B  is  above  A,  together 
with  the  maximum  tension,  T,  in  the  wire  at  the  point  of  support  B, 
we  can  determine  the  reactions  at  both  of  the  supports  and  also  the  sag 
in  the  wire. 

The  wire  ADRB  is  in  equilibrium  under  three  forces;  viz.,  the  ten- 
sions acting  at  A  and  B  in  the  directions  of  the  tangents,  and  its  weight 
w/1  acting  at  its  center  of  gravity.  These  three  forces  intersect  at  the 
point  Z,  and  the  vertical  line  through  this  point  passes  also  through 
the  point  C  on  the  line  AB  and  midway  between  A  and  B.  On  this 
vertical  line  lay  off  the  distance  OU  equal  to  W  or  w/1,  and  let  it  be 
bisected  at  the  point  C  so  that  OC  equals  CU  or  J/£  w/1.  Complete  the 
force  diagram  by  drawing  UV  and  OV  parallel  respectively  to  ZB  and 
AZ.  UV  will  then  be  the  tension  in  the  wire  at  the  point  B,  and  OV 
will  be  the  tension  at  the  point  A.  The  vertical  component  of  the  re- 
action at  B  is  the  vertical  component  of  UV  and  is  equal  to  UM. 
The  vertical  component  of  the  reaction  at  A  is  the  vertical  component 
of  OV  and  is  equal  to  MO  or  UO  —  UM. 

Complete  the  parallelogram  of  forces  by  drawing  OF  parallel  to  UV 
and  FU  parallel  to  OV.  The  points  F  and  V  must  lie  on  the  line  AB. 
Let  the  tension  UV  in  the  wire  at  the  point  B  be  denoted  by  T.  Let 
0  be  the  angle  made  by  the  line  AB  with  the  horizontal  line  AX,  and 
let  </>  be  the  angle  between  the  lines  FO  and  AB.  Let  ,3  be  the  angle 
which  the  tangent  at  the  point  B  makes  with  the  horizontal  plane. 

Angle  O  C  F  =  ft  +  90°. 


Sin  <p  =          -  Sin  (90°  +  *)  =          cos 
But 

71 

1    = 


.  -'/wA 

an    ^j 


The  horizontal  component  of  the  stress  in  the  wire  at  either  point  of 
support,  is  H  =  T  Cos  fi.  This  is  also  the  total  tension  in  the  wire  at 
the  point  (if  any)  where  the  slope  of  the  wire  is  zero.  The  total  stress 
in  the  wire  is  greatest  at  the  highest  point  B,  and  the  vertical  com- 
ponent of  the  reaction  at  this  point  is  UM  =  NO  =  T  Sin  fi. 


Transmission  Towers  29 

The  weight  supported  by  the  lower  tower  is  MO  =  w/1  --  T  Sin  /?. 

In  some  cases  this  may  be  zero,  or  it  may  even  be  a  negative  quan- 
tity, in  which  case  the  wire  will  exert  an  upward  pull  on  the  lower  sup- 
port. In  that  case  the  sag  S  below  the  point  A  will  be  zero.  This  is 
not  an  unusual  condition  on  a  steep  incline,  or  on  a  moderate  incline  if 
the  spans  are  short. 

The  position  of  the  lowest  point  D  in  the  span  is  determined  by  the 
condition  that  the  vertical  component  of  the  force  acting  at  either  point 
of  support  is  the  weight  of  that  part  of  the  wire  between  the  point  D 
and  the  point  of  support.  This  is  true  because  the  tension  in  the  wire, 
at  the  point  D,  has  no  vertical  component.  The  horizontal  distance 
of  the  point  D  from  the  support  B,  is, 

ON       /  -  T  Sin  ,3  _  T  Sin  ,3  •  cos  " 
*  OU  =          w/1  w 

It  may  happen  that  /B  will  be  found  to  be  equal  to  or  greater  than  /, 
in  which  case  the  support  A  will  be  the  lowest  point  in  the  span.  If 
the  vertical  component  of  the  force  at  the  support  B  is  greater  than  the 
total  weight  of  the  span  (w/1),  it  follows  that  the  resultant  force  at  the 
support  A  will  be  in  an  upward  direction. 

The  total  sag  is  S  +  h.  The  value  of  this  sag  may  be  determined  by 
considering  /„  to  be  one-half  of  a  span  having  supports  at  the  same 
level,  and  having  the  sag, 

Q  m      -J5L_    (2_W!          w/,1 

cos  0  '    8  H         2  H  cos  ft ' 

STRINGING  WIRES  IN  SPANS  ON  STEEP  GRADES 

When  transmission  lines  are  carried  up  steep  grades,  and  are  strung 
on  towers  in  such  a  manner  that  the  lower  support  A  is  the  lowest  point 
of  the  span,  it  is  of  considerable  advantage  in  stringing  the  wires,  to 
know  the  maximum  deflection  of  the  wire  from  the  straight  line  AB  as 
observed  by  sighting  between  the  points  A  and  B.  Such  a  condition 
is  shown  in  Fig.  9. 

A  line  drawn  tangent  to  the  curve  and  parallel  to  the  line  AB  will  be 
tangent  at  the  point  R,  which  is  on  a  vertical  line  drawn  through  the 
point  C  at  the  middle  of  the  line  AB.  The  wire  will,  therefore,  have 
its  maximum  deflection  from  the  line  AB  at  this  point  R.  The  hori- 
zontal projections  of  AR  and  RB  are  equal,  and  have  the  value  Yd 
when  the  horizontal  projection  of  the  span  AB  is  /. 


30 


Transmission  Towers 


Fig.  9 

Let  the  deflection  of  the  wire,  at  the  point  R,  from  the  straight  line 
AB  be  denoted  by  S1.  By  taking  moments  about  the  point  A,  and 
putting  their  sum  equal  to  zero,  we  may  determine  the  value  of  this 
deflection. 

w/1 

2 

L 

4 


H 


S1  =  ^f 


/ 
4°r 


w/1 

2 


ci  


H 


w/2 
8H 


Comparing  this  span  with  a  span  having  the  same  horizontal  pro- 
jection but  supports  A  and  B1  at  the  same  level,  it  will  be  seen  that 
when  a  wire  is  strung  between  supports  on  a  slope,  the  maximum  deflec- 
tion S1  of  that  wire  from  the  straight  line  joining  the  two  points  of  sup- 
port, is  exactly  the  same  as  the  maximum  sag  S  of  the  same  wire  when 
strung  between  points  on  the  same  level ;  provided  the  span  measured 
horizontally  and  the  horizontal  component  H  of  the  tension  are  the 
same  in  both  cases. 

The  above  analysis  will  also  show  that  this  relationship  between 


Transmission  Towers  31 

spans  having  the  same  horizontal  projections  will  be  true  even  though 

the  lowest  point  on  the  wire  is  not  coincident  with  the  lower  support. 

These  formulas  for  lines  carried  up  steep  inclines  are  all  based  on  the 

assumption  that  the  total  weight  of  wire  is  the  weight  per  foot  of  length 

of  wire  multiplied  by  the  length  of  the  line  AB  (which  is  I1  =  -    — ). 

cos  " 

This,  of  course,  is  an  approximation  which  is  the  more  nearly  correct 
as  the  sag  is  kept  small  in  proportion  to  the  span. 

Having  determined  the  value  of  S1,  and  knowing  the  value  of  0, 
we  may  determine  the  value  of  CR.  This  distance  can  then  be 
measured  down  vertically  below  the  points  of  support  A  and  B,  as 
shown  at  F  and  K,  and  the  wire  when  strung  between  these  two  sup- 
ports may  be  drawn  up  until  it  becomes  tangent  to  the  line  FK  parallel 
to  AB  and  at  the  distance  CR  vertically  below  AB.  This  may  be 
observed  by  sighting  from  F  to  K. 

The  length  of  the  wire  between  fixed  supports  at  the  same  horizontal 
level  is  approximately, 

8  S2 

L  =  /  +  % 

in  which  /  is  the  distance  between  supports  and  S  the  sag  at  the  center, 
both  expressed  in  feet.  In  the  case  of  a  wire  between  supports  which 
are  not  on  the  same  level,  the  total  length  may  be  considered  to  be 
made  up  of  two  distinct  parts  of  the  parabolic  curve. 

RELATION  BETWEEN  STRESS,  TEMPERATURE  AND  SAG 

All  of  the  formulas  so  far  deduced  for  determining  working  condi- 
tions for  the  wires  on  the  basis  of  using  parabolic  curves,  have  been 
obtained  by  ignoring  the  fact  that  the  wires  are  elastic  and  will  there- 
fore stretch  under  tension,  and  that  the  length  will  also  be  affected  by 
changes  in  temperature. 

It  is  customary  to  assume  that  the  material  of  the  conductors  is 
perfectly  elastic  up  to  a  certain  critical  stress,  known  as  the  elastic 
limit,  and  that  the  process  of  elongation  and  contraction  follows  a 
straight  line  law.  Therefore,  the  length  of  the  wire  will  be  changed  by 
the  amount  of  elongation  or  contraction  which  will  be, 

-L     ^ 

L  .    £, 

in  which  Le  is  the  elongation  or  contraction,  L  is  the  unstressed  length 


32  Transmission  Towers 

of  wire,  Te  is  the  stress  per  square  inch  in  the  wire,  and  E  is  the  modulus 
of  elasticity. 

The  change  in  length  due  to  differences  of  temperature  will  be, 

Lt  =  Lo  (1  +  mt), 

in  which  L0  is  the  original  length,  t  is  the  number  of  degrees  Fahrenheit 
change  in  temperature,  and  m  is  the  coefficient  of  expansion  for  the 
material  in  the  conductor.  These  two  changes  in  length  of  wire  are 
not  independent  of  each  other.  They  act  simultaneously  and  are 
inter-related,  and  must  be  considered  together.  Any  temperature 
variation  causes  a  change  in  the  length  of  wire,  which,  in  turn,  changes 
the  sag  condition,  and  hence  changes  the  stress,  which,  in  turn,  will 
affect  the  amount  of  change  in  length  of  wire  due  to  the  stress  in  it. 

In  the  case  of  long  spans  it  is  always  necessary  to  make  proper  allow- 
ances for  the  changed  outline  of  curve  assumed  by  wires,  due  both  to 
their  elasticity  and  to  the  elongation  or  contraction  resulting  from 
changes  in  temperature.  This  is  also  advisable  oftentimes  in  the  case 
of  comparatively  short  spans,  especially  where  a  minimum  clearance 
is  required  under  the  lowest  wires  under  the  worst  conditions  of  load- 
ing. This  matter  has  been  the  subject  of  quite  extensive  investiga- 
tion on  the  part  of  several  different  men,  and  several  different  solutions 
of  the  problem  have  been  offered.  No  theoretically  correct  analytical 
solution  that  is  easy  of  application  has  yet  been  found,  but  every  one  is 
based  on  assumptions  which  involve  some  approximations.  The  first 
assumption  generally  made  is  that  the  parabola  approximates  near 
enough  to  the  true  curve  in  which  the  wire  hangs.  For  short  spans 
this  is  not  much  in  error,  but  on  the  longer  spans  the  difference  in  re- 
sults obtained  by  figuring  the  curve  first  as  a  parabola  and  then  as  a 
catenary,  is  very  considerable,  especially  when  changes  due  to  the 
elasticity  of  the  wire  and  to  differences  in  temperature  are  taken  into 
account. 

Some  mathematical  expressions  have  been  worked  out  for  taking 
care  of  these  conditions  approximately,  but  they  all  involve  the  first 
and  third  powers  of  the  unknown  quantity.  It  is  a  tedious  matter  to 
solve  such  equations,  which  is  another  reason  why  they  are  not  satis- 
factory, especially  when  it  is  known  in  advance  that  the  result,  when 
obtained,  will  not  be  accurate. 


Transmission  Towers  33 

THOMAS'  SAG  CALCULATIONS 

After  having  studied  several  of  these  different  solutions,  the  writer 
is  of  the  opinion  that  the  best  one  is  the  semi-graphical  method  offered 
by  Percy  H.  Thomas  in  his  article  on  "Sag  Calculations  for  Suspended 
Wires,"  which  was  presented  at  the  28th  Annual  Convention  of  the 
American  Institute  of  Electrical  Engineers,  and  which  was  published 
in  their  "Transactions  for  1911."  Thomas  uses  the  true  catenary,  and, 
at  the  same  time,  takes  care  of  all  changes  in  the  loading  conditions. 
He  attacks  the  given  problem  by  first  reducing  the  span  in  size,  with- 
out changing  the  shape  of  the  curve,  until  the  span  is  one  foot.  Having 
determined  all  the  conditions  attending  the  problem  for  the  similar 
span  of  one  foot  length,  it  is  then  an  easy  matter  to  convert  these  into 
corresponding  quantities  for  the  given  span. 

When  the  span  is  reduced  in  size  without  changing  the  shape  of  the 
curve,  the  sag  will  be  reduced  in  direct  proportion  to  the  reduction  of 
span;  in  other  words,  the  percentage  of  sag  will  remain  the  same. 
The  stress  in  the  wire  and  the  length  of  wire,  also,  will  be  reduced  in 
the  same  ratio.  Again,  the  stress  in  the  wire  for  a  given  span  for  a 
definite  sag  is  directly  proportional  to  the  total  load  per  foot  on  the 
wire. 

Taking  advantage  of  this  fact,  two  curves  can  be  plotted  which  will 
give  the  sag,  stress  and  length  relationships  for  a  wire  on  which  the 
total  load  is  one  pound  per  foot  when* strung  over  a  one-foot  span,  as 
shown  in  Fig.  10.  These  relationships  will  be  directly  proportional 
to  those  obtaining  for  the  longer  spans  and  for  the  varied  loadings 
per  foot  of  length  on  the  wire  used.  Different  sets  of  curves  may  be 
plotted  for  different  proportions  of  sags  to  spans.  A  careful  study  of 
these  curves  will  show  how  the  stress  changes  with  increase  of  sag.  It 
will  be  noted  that  after  the  sag  has  reached  15%  to  20%  there  is  little 
reduction  in  stress  by  further  increase  of  sag,  and  that  an  actual  in- 
crease of  stress  soon  results.  This  is  of  extreme  importance  when 
considering  the  use  of  very  light  wires  on  long  spans. 

The  sine  of  the  angle  made  by  the  wire  with  the  horizontal,  at  the 
point  of  support,  is  one-half  the  length  of  wire  in  the  span  divided  by 
the  stress  with  one  pound  per  foot  weight  of  wire,  and  may  be  obtained 
from  the  length  curve. 


34 


Transmission  Towers 


THOMAS'  CURVES  FOR  SAG  AND 

These  curves  are  plotted  from  computations  made  on  the  assump- 
tion that  the  sag  curve  is  a  catenary.  They  have  the  properties  of  a 
catenary  assumed  by  a  wire  weighing  one  pound  per  foot  of  length 
when  strung  between  supports  at  the  same  level  and  one  foot  apart. 
The  abscissas  of  these  curves  give  the  sag  and  length  corresponding 
to  one  ordinate  which  is  the  stress  factor  that  is  common  to  both 
of  them. 

The  following  example  will  demonstrate  the  use  of  the  curves. 
Span  =  500  feet;  maximum  stress  allowed  in  the  wire  at  the  points 
of  support  =  1800  pounds;  weight  per  foot  of  wire,  including  any 
ice  or  insulation  coating  combined  with  wind  load  =1.5  pounds 
per  foot.  The  stress  factor  for  the  curves  is  the  equivalent  stress 
in  a  wire  weighing  one  pound  per  foot  and  having  a  one-foot  span . 
This  is  obtained  by  dividing  the  allowable  stress  in  the  given  wire  by 
the  product  of  the  span  in  feet  and  the  weight  per  foot  of  the  wire 


In    this    case  it  is 


1800 


2.4.      This    is   the 


500  X  1.5 

stress  factor  which  is  the  ordinate  to  both  of  the  curves. 
The  horizontal  line  through  this  value,  2.4,  intersects  the 
sag  curve  at  a  point  of  which  the  abscissa  is  .0535,  and  the 
length  curve  at  a  point  of  which  the  abscissa  is  1.0076. 
These  values  are  for  a  one-foot  span,  and  the  required  values 
for  the  given  span  are  obtained  by  multiplying  these  values 
by  the  length  of  the  given  span.    The  required  sag  for  the 
500  foot  span  is  therefore  500  x  .0535  =  26.75  feet,  and  the 
length  is  500  x  1.0076  =  503.80  feet    .In  case  the  allowable 
or    length    of   wire  had    been   given    instead   of  the 
stress,   the  operation  would   have  been  reversed. 
The    abscissa   corresponding    to    the    given  value 
would  then  locate  a  point  on  the  curve,  and  a  hori- 
zontal line  through  this  point  would  intersect  the 
stress  factor  line  of  ordinates  at  a  point  whose  value 
when  multiplied  by  the  span  in  feet  and  the  weight 
foot   of    the    wire    in    pounds    would    equaj 
the  stress  in  the  wire  at  each  point  of  sup- 
port.   Had  the  sag  of  26.75  feet  been  given, 
the    abscissa   for   the    sag  curve  would  be 
obtained    by    dividing   26.75  by 
500  giving  a   quotient   of   .0535. 
A  horizontal  line  through  the  sag 
curve  at  a  point 
having  abscissa 
=     .0535  would 


WOO 


1.00! 


Transmission  Towers 


35 


STRESS  CALCULATIONS  (FIG.  10) 

intersect  the  stress  factor  line  of  ordinates  at  2.4.     This  value  when  multiplied  by  the  span  in  feet  and 
the  weight  of  the  wire  per  foot  in  pounds  would  give  the  desired  stress,  thus; 

2.4  x  500  x  1.5  -  1800 
Variations  in  Loading 

Assume  the  load  to  decrease  from  1.5  to  0.5  Ib.  per  ft.,  the  temperature  remaining  the  same.  The 
resulting  conditions  of  Stress,  Sag  and  Length  are  determined  as  follows.  If  all  the  load  could  be 
removed  from  the  wire  it  would  contract  to  its  "unstressed"  Ungth,  called  Lo,  from  its  full-load  length, 
L  =  1.0076  ft.  per  foot  of  span.  If  the  sectional  area  of  the  conductor  =  .03  sq.  in.;  the  coefficient  of 
elasticity  —  E  =  16,000,000.  and  the  total  stress  =  1800  Ib..  then, 

1800 


L  =  1.0076  =  Lo  +  «*  ,^/wwv  X  U, 

=  1.003836  tt.  for  one-foot  span. 


1.0076 
1.00375 


T  16,000,000 
from  which, 

T  1.0076 

1800 

1    .     ~03" 
T  16,000,000 

Plot  this  on  the  zero  Stress  Factor  line,  at  Lo.  Then  the  line  LoL  is  the  "stress-stretch"  line  for  this 
particular  span  and  loading.  If  the  load  of  1.5  Ib.  per  ft.  stretches  the  wire  for  one-foot  span  from  Lo  to 

L,  a  load  of  0.5  Ib.  per  ft.  will  stretch  it  p|  (L  —  Lo)  =  H  (1.0076—1.003836)  =  .001255  ft.,  which, 

added  to  Lo,  gives  the  length  of  the  wire  for  the  lighter  load,  1.005091  ft.  for  one-foot  span.  Plot  this 
value  on  the  same  Stress  Factor  line  as  for  the  preceding  load,  S.  F.  =  2.4,  and  through  this  point  and 
Lc  draw  a  line  to  the  Length  curve.  Its  intersection,  Li  =  1.00533,  is  the  length  of  the  wire  for  one- 
foot  span  for  a  load  of  0.5  Ib.  per  ft.  For  this  new  condition  the  properties  of  the  500  ft.  span  will  be: 
Stress  =  500  x  2.85  x  0.5  =713  Ib.;  Length  =  500  x  1.00533  =  502.665  ft.;  and  Sag  =  500  x  .0445  - 
22.25  ft.  This  operation  is  reversed  when  working  from  a  light  to  a  heavier  load,  the  principle  being 
the  same  in  all  cases. 

Temperature  Variation 

The  preceding  methods  assume  a  constant  temperature,  but  every  change  of  temperature  causes  a 
readjustment  of  Stress,  Sag  and  Length  in  any  span.  To  determine  the  new  conditions,  first  find  Lo. 
the  "zero  stress"  length  of  wire  for  one-foot  span,  as  above  described.  Then  compute  the  change  in  this 
length  resulting  from  the  change  of  temperature,  and  plot  this  variation  from  Lo  along  the  zero 
Stress  Factor  line.  This  gives  the  "unstressed"  length  for  the  new  temperature,  and  through  this  point 
draw  a  line  parallel  to  the  "stress-stretch"  line  for  the  load  then  existing.  Its  intersection  with  the 
Length  curve  gives  the  new  length  of  wire  for  one-foot  span,  and  determines  the  other  factors.  For 
example,  if  the  above  computation  was  for  a  temperature  of  0°  F.,  and  the  properties  of  the  span  are 
required  for  20°  intervals  to  100°  F.,  and  the  coefficient  of  heat  expanison  is  .0000096,  the  length  at 
20°  F.  will  be. 

LJOO    =  L»  (1  +  .0000096  t)  -  1.003836  (1   +  .0000096  X  20)   =  1.004029  ft. 

Through  this  new  length  draw  a  line  parallel  to  line  LoLi.  It  intersects  the  Length  curve  at  1.005505, 
the  coincident  values  being:  Stress  Factor  =  2.8,  Sag  =  .0453.  Then  for  the  500  ft.  span,  Stress  = 
500  X  2.80  X  .5  =  700  Ib.,  Length  =  500  X  1.005505  =  502.7525  ft..  Sag  =  500  X  .0453  =  22.65  ft. 
Similarly  for  successive  20°  intervals,  OF  for  any  other  temperature  changes. 


10." 


36 


Transmission  Towers 


VALUES  USED  FOR  PLOTTING  CURVES  FOR   WIRE    WEIGHING   ONE 
POUND  PER  FOOT  OF  LENGTH  WHEN  SUSPENDED  IN  ONE-FOOT  SPAN 


Y  =^iec 


Stress 

Sag  =  Y  -  C 

Length  =  2  X 


_x 

c 


') 


X 

c 

Stress 

Sag 

Length 

2c 
c 

Stress 

Sag 

Length 

.0050 
.0055 
.0060 
.0065 

100.001  3 
90.910  5 
83.334  8 
76.924  7 

.001  250 
.001  375 
.001  500 
.001  625 

1.000  004  2 
1.000  005  1 
1.000  006  1 
1.000  007  1 

.080 
.085 
.090 
.095 

6.270  0 
5.903  6 
5.578  1 
5.286  9 

.020  01 
.021  26 
.022  52 
.023  77 

1.001  066 
1.00  1  205 
1.001  351 
1.  001  503 

.0070 
.0075 
.0080 
.0085 

71.430  3 
66.668  5 
62.502  0 
58.825  7 

.001  750 
.001  875 
.002  000 
.002  125 

1.000  008  2 
1.000  009  4 
1.000  010  7 
1.000  012  0 

.100 
.105 
.110 
.115 

5.025  0 
4.788  2 
4.573  0 
4.376  6 

.025  02 
.026  27 
.027  53 
.028  78 

1.001  668 
1.001  839 
1.002  017 
1.002  205 

.0090 
.0095 
.010 
.011 

55.557  8 
52.633  9 
50.002  5 
45.457  3 

.002  250 
.002  375 
.002  50 
.002  75 

1.000  013  5 
1.000  015  0 
1.000  017 
l.COO  020 

~120 
.125 
.130 
.135 

4.196  7 
4.031  3 
3.878  7 
3.734  2 

.030  04 
.031  29 
.032  55 
.033  80 

1.002  402 
1.002  606 
1.002  819 
1.003  040 

.012 
.0125 
.013 
.014 

41.669  7 
40.003  1 
38.464  8 
35.717  8 

.003  00 
.003  13 
.003  25 
.003  50 

1.000  025 
1.000  026 
1.000  028 
1.000  033 

.140 
.145 
.150 
.170 

3.606  5 
3.484  6 
3.370  9 
2.983  8 

.035  06 
.036  31 
.037  57 
.042  60 

1.003  270 
1.003  508 
1.003  754 
1.004  825 

.015 
.016 
.017 
.0175 

33.337  1 
31.254  0 
29.416  0 
28.575  8 

.003  75 
.004  00 
.004  25 
.004  38 

1.000  037 
1.000  043 
1.000  048 
1.000  051 

.200 
.220 
.25 
.27 

2.550  2 
2.328  0 
2.062  8 
1.919  8 

.050  17 
.055  22 
.062  83 
.067  91 

1.006  680 
1.008  086 
1.010  444 
1.012  194 

.018 
.019 
.020 
.022 

27.782  3 
26.320  5 
25.005  0 
22.732  8 

.004  50 
.004  75 
.005  00 
.005  50 

.000  054 
1.000  060 
1.000  067 
1.000  081 

.30 
.32 
.35 
.37 

1.742  2 
1.643  2 
1.517  0 
1.444  9 

.075  56 
.080  68 
.088  40 
.093  56 

1.015  068 
1.017  154 
1.020  542 
1.022  973 

.024 
.025 
.026 
.028 

20.839  3 
20.006  3 
19.237  3 
17.864  1 

.006  00 
.006  25 
.006  50 
.007  00 

1.000  096 
.000  104 
.000  113 
.000  131 

.40 
.42 
.45 

.47 

1.351  3 
1.297  0 
1.225  5 
1.183  5 

.101  34 
.106  55 
.114  41 
.119  68 

1.026  881 
1.029  660 
1.034  093 
1.037  224 

.030 
.032 
.034 
.036 

16.674  2 
15.633  0 
14.714  4 
13.897  9 

.007  50 
.008  00 
.008  50 
.009  00 

.000  150 
.000  171 
.000  193 
1.000  216 

.50 
.55 
.60 
.70 

1.127  6 
1.050  1 
.987  9 
.896  5 

.127  63 
.141  00 

.154  55 
.182  26 

1.042  19 
1.051  19 
1.061  09 
1.083  69 

.038 
.040 
.043 
.047 

13.167  4 
12.510  0 
11.638  7 
10.650  1 

.009  50 
.010  00 
.010  75 
.011  75 

1.000  241 
1.000  267 
1.000  308 
1.000  368 

.80 
.90 
1.00 
1.10 

.835  8 
.796  2 
.771  54 
.758  42 

.210  83 
.240  61 
.271  54 
.303  87 

.110  13 
1.140  57 
.175  20 
.214  23 

.050 
.055 
.060 
.065 

10.012  5 
9.104  7 
8.348  3 
7.708  4 

.012  50 
.013  75 
.015  00 
.016  26 

1.000  417 
1.000  504 
1.000  600 
1.000  704 

1.20 

1.30 
1.40 
1.50 

.754  44 
.758  04 
.768  18 
.784  14 

.337  77 
.373  43 
.411  04 
.450  80 

.257  88 
.306  45 
.360  21 
.419  52 

.070 
.075 

7.160  4 
6.685  4 

.017  51 
.018  76 

1.000  817 
1.000  938 

1.60 

.805  46 

.492  96 

1.484  73 

Transmission  Towers  37 

Considering  the  case  of  a  s£>an  having  supports  at  unequal  heights 
above  a  given  horizontal  plane,  if  the  horizontal  distance  from  the 
higher  support  to  the  lowest  point  of  the  wire  is  known,  the  stress  and 
sag  in  this  part  of  the  span  can  be  determined  by  considering  this  part 
as  one-half  of  a  span  equal  to  twice  this  distance.  The  smaller  stress 
in  the  other  part  can  be  determined  in  the  same  manner. 

The  following  formulas,  based  upon  the  catenary,  give  the  horizontal 
distance  from  the  higher  support  to  the  lowest  point  of  the  wire, 

.    I   ,  hT      h_«  (A) 

1>U 


-h  +  V~d  (B) 

where, 

/  =  the  span  in  feet. 
/u  =  the  horizontal  distance  in  feet  from  the  higher 

support  to  the  lowest  point  of  the  wire, 
h  =  the  difference  in  height  of  the  two  supports  in 

feet. 
T  =  the  stress  in  pounds  in  the  wire  at  the  higher 

support,  with  one  pound  per  foot  load  on  the 

conductor, 
d  =  the  sag  in  feet  measured  from  the  higher  point 

of  support. 

Formula  (A)  is  useful  when  the  span  and  the  stress  to  be  allowed  in 
the  wire  are  given,  and  formula  (B)  when  the  span  and  the  sag  are 
given. 

These  formulas  are  approximate  in  that  the  horizontal  projection  of 
the  wire  is  substituted  for  the  actual  length  of  it.  Formula  (A)  is 
correct  within  from  2%  to  4%,  when  neither  sag  nor  difference  in 
heights  of  supports  exceeds  15%  of  the  span.  Formula  (B)  has  an 
error  of  less  than  1%  under  these  conditions. 

SPACING  OF  TOWERS 

The  problem  of  determining  the  type  and  the  spacing  of  the  towers 
to  be  used,  is  one  that  requires  considerable  study  of  all  the  foregoing, 
as  the  towers  are  only  a  part  of  the  complete  installation,  and  a  saving 
on  one  item  may  easily  be  more  than  offset  by  an  increased  cost  of 


38  Transmission  Towers 

some  other  items  affected  by  the  same  conditions  which  made  the 
initial  saving.  In  other  words,  it  is  a  case  of  balancing  one  condition 
against  another,  to  determine  what  is  the  best  possible  combination. 
The  supporting  structures  must,  of  course,  be  placed  as  far  apart  as 
possible;  but  an  analysis  of  the  various  sag  conditions  for  the  wires 
makes  it  evident  that  there  are  definite  limits  to  be  observed. 

SPACING  OF  CONDUCTORS 

After  the  spacing  of  towers  has  been  determined,  together  with  the 
size  of  wires  to  be  used  and  the  voltage  to  be  carried  by  them,  the  next 
thing  to  consider  is  the  spacing  of  the  several  wires  and  the  minimum 
clearance  from  the  ground  line  to  the  lowest  wire  under  the  worst 
loading  condition.  The  maximum  sag  to  be  allowed  must  then  be 
determined,  and  this  condition,  along  with  the  assumed  loading  across 
the  line,  will  determine  the  pull  which  may  occur  in  the  direction  of  the 
line  on  the  wire.  The  spacing  of  the  wires  in  both  horizontal  and 
vertical  directions  is  dependent  upon  the  voltage  carried  and  upon  the 
length  of  spans.  The  minimum  spacing,  especially  in  the  horizontal 
direction,  will  obtain  when  the  wires  are  supported  on  pin  insulators, 
or  are  attached  to  the  cross  arms  by  means  of  strain  insulators.  For 
this  condition,  it  is  recommended  that,  for  conductors  carrying  alter- 
nating current,  the  minimum  separation  of  these  conductors,  at  the 
points  of  support,  shall  be  one  inch  for  every  twenty  feet  of  span,  and 
one  inch  additional  for  each  foot  of  normal  sag,  but  in  no  case  shall  the 
separation  be  less  than : 

Line  Voltage  Clearance 

Not  exceeding  6600  volts .. . 14J/2  inches 

Exceeding    6600  volts  but  not  exceeding  14000  volts,  24      inches 
14000     "       "      "  "         27000     "      30 

27000    •"       "      "  35000     "      36 

35000     "       "      "  47000     "      45 

47000     "       "      "  70000     "      60 

For  voltages  higher  than  70000  the  minimum  separation  should  be 
60  inches  plus  0.6  inch  for  every  additional  1000  volts. 


Transmission  Towers  39 

When  conductors  are  supported  by  suspension  insulators,  the  separa- 
tion of  them  horizontally  must  be  made  greater  than  when  they  are 
supported  on  pin  type  insulators.  The  amount  of  this  increase  is 
empirical,  and  is  more  or  less  a  matter  of  judgment  on  the  part  of  the 
Engineer  who  designs  the  line.  When  the  conductor  wire  is  supported 
from  the  cross  arm  by  strain  insulators,  it  is  frequently  assumed  that 
the  jumper  wire  will  swing  to  a  position,  making  an  angle  of  thirty 
degrees  with  the  vertical.  It  is  usually  assumed  that  the  maximum 
swing  of  a  suspension  insulator  string  will  be  to  an  angle  of  forty-five 
degrees,  but  this  depends  upon  the  size  and  weight  of  the  conductor, 
and  also  upon  the  assumed  maximum  loading.  It  is  possible  that 
under  unusually  severe  conditions,  two  wires  suspended  from  the  same 
cross  arm  may  swing  toward  each  other  until  each  of  them  will  make 
an  angle  of  about  thirty  degrees  with  the  vertical.  Or  even  though 
they  do  not  both  swing  the  same  amount,  it  is  a  safe  assumption  that 
twice  the  horizontal  projection  of  the  length  of  one  insulator  string 
when  swung  to  thirty  degrees  from  the  vertical,  will  be  equivalent  to 
the  sum  of  the  horizontal  projections  of  the  two  wires  when  swinging 
toward  each  other  under  the  worst  conditions  of  service.  This  means 
that  when  wires  are  supported  by  suspension  insulators  instead  of  on 
pin  type  insulators,  the  horizontal  separation  should  be  increased  by 
the  length  of  one  insulator  string. 

It  is  generally  recommended  that  the  minimum  clearance  in  any 
direction  between  the  conductors  and  the  tower,  shall  not  be  less  than : 

Line  Voltage  Clearance 

Not  exceeding  14000  volts 9  inches 

Exceeding  14000  but  not  exceeding  27000 15     " 

27000    "      "  35000 18     " 

35000    "      "  47000 21     " 

47000    "     V  7000° ....24     " 

Usually  the  suspension  insulators  are  made  sufficiently  long  so  that 
when  swung  out  to  the  assumed  position  of  maximum  swing,  the  ver- 
tical distance  between  the  conductor  and  its  supporting  cross  arm, 
or  any  other  part  of  the  tower,  will  meet  all  the  requirements  for 
clearance.  The  overhead  ground  wire,  or  wires,  should  be,  in  general, 
not  more  than  forty-five  degrees  from  the  vertical  through  the  adjoin- 
ing conductor. 


40  Transmission  Towers 

The  several  wires  must  be  spaced  far  enough  apart  vertically  so  that 
under  the  worst  conditions  the  wires  will  not  come  so  close  together  as 
to  make  trouble  electrically.  This  must  have  careful  consideration, 
especially  on  the  very  long  spans,  because  it  is  entirely  possible  during 
storms  for  the  lowest  wires  to  be  free  from  ice  loading  or  to  be  suddenly 
relieved  of  such  loading,  when  they  might  swing  up,  close  to  the  wires 
directly  above  them,  which  might  be  heavily  loaded  with  ice  and 
hence  have  considerable  sag. 

The  arrangement  and  spacing  of  the  wires  almost  always  fixes,  with- 
in certain  limits,  the  general  type  of  the  supporting  structure  to  be 
used.  This  is  at  least  true  of  the  upper  part  of  it.  The  outline  of  the 
structure  below  the  lowest  cross  arm  will  be  made  that  which  is  the 
most  economical,  unless  such  an  outline  is  prohibitive  on  account  of 
right-of-way  or  other  limiting  conditions. 

Where  the  transmission  line  consists  of  three  conductor  wires,  with 
or  without  a  ground  wire,  it  very  often  works  out  to  very  good  advan- 
tage to  put  the  three  conductor  wires  in  the  same  horizontal  plane, 
which  means  that  the  middle  one  will  pass  through  the  tower.  When 
suspension  insulators  are  used  with  this  arrangement  of  wires,  the 
tower  must  be  made  wide  enough  to  allow  ample  clearance  from  the 
conductor  when  swung  to  maximum  position  either  way.  But  if 
strain  insulators  are  used,  then  a  much  narrower  jtower  may  be  used  by 
attaching  the  jumper  wire  to  a  pin  on  the  center  line  of  the  tower. 
The  narrower  tower  makes  a  much  more  economical  construction. 
When  six  conductor  wires,  with  or  without  ground  wires,  are  used, 
three  of  the  conductors  are  placed  on  each  side  of  the  tower.  These  are 
generally  placed  so  that  the  three  wires  in  each  set  are  in  the  same 
vertical  plane,  but  sometimes  the  middle  one  will  be  put  farther  from 
the  center  line  of  the  tower  than  the  other  two  wires. 

The  design  of  the  supporting  structures  from  this  point  on,  consists  in 
determining  just  what  loads  are  to  be  considered  as  coming  on  the 
structures,  what  unit  stresses  shall  be  used  throughout,  and  whether  a 
com  para  tirely  large  or  small  investment  shall  be  put  into  them.  In 
other  words,  it  is  a  matter  of  first  importance  whether  these  struc- 
tures are  to  be  regarded  for  a  temporary  proposition,  and  hence  made 
as  cheaply  as  possible,  or  whether  they  are  to  be  considered  as  part  of 
a  permanent  construction  and  therefore  figured  a  little  more  liberally. 


Transmission  Towers  41 

TEMPORARY  STRUCTURES 

For  a  temporary  proposition  the  structures  are,  of  course,  made  as 
light  as  possible  and  are  almost  always  painted.  They  are  rarely  gal- 
vanized. In  such  cases  the  assumed  loadings  are  kept  very  low,  and 
are  intended  to  take  care  of  only  normal  conditions,  on  the  theory  that 
if  some  of  the  structures  should  be  subjected  to  loadings  of  unusual 
intensity  resulting  from  specially  severe  storms,  it  will  be  more  eco- 
nomical to  replace  some  of  them  that  might  be  destroyed  than  to  provide 
additional  strength  in  all  the  supports.  For  the  same  reason  the  unit 
stresses  are  always  run  as  high  as  possible. 

PERMANENT  STRUCTURES 

On  the  other  hand,  where  permanency  of  construction  is  wanted, 
the  design  is  made  more  liberal  in  every  way.  To  start  with,  the 
assumed  loadings  are  such  as  will  be  expected  to  take  care  of  more  than 
ordinary  conditions  of  service.  They  will  be  made  sufficiently  high  to 
be  in  themselves  an  insurance  against  possible  interruptions  of  service 
due  to  breakdowns  caused  by  storms.  Also,  the  unit  stresses  will  be 
kept  lower  and  heavier  material  will  be  specified.  Generally,  but  not 
always,  such  structures  will  be  required  to  be  galvanized  instead  of 
painted,  so  that  the  structure  will  be  in  service  for  a  longer  time. 

THICKNESS  OF  MATERIAL 

When  the  material  is  required  to  be  galvanized,  many  specifications 
will  allow  web  members  to  be  made  of  material  only  y%  "thick,  but  will 
require  a  minimum  thickness  of  •£$*  or  possibly  %"  for  the  main  posts. 
Almost  all  specifications  require  a  minimum  thickness  of  material  of 
TS*  for  all  members  when  painted;  but  some  specify  that  no  material 
less  than  %  "  thick  shall  be  used  when  painted ;  while  others  demand  a 
minimum  thickness  of  y\r"  for  all  material,  regardless  of  whether  it  is 
painted  or  galvanized. 

GALVANIZE  FOR  PERMANENCY 

The  history  of  transmission  line  structures  proves  that  where  per- 
manency of  construction  is  desired,  they  should  always  be  galvanized, 
not  painted.  At  least  all  parts  of  the  structure  in  close  proximity  to 
the  conductor  wires  should  be  galvanized,  irrespective  of  what  kind  of 
a  protective  coating  is  given  to  the  balance  of  the  structure.  This  is 
especially  true  in  those  cases  where  high  voltages  are  used. 


42  Transmission  Towers 

SPECIFICATIONS  FOR  DESIGNS 

There  is  no  such  thing  as  a  standard  practice  among  Engineers 
today  regarding  the  method  to  be  pursued  in  preparing  specifications 
for  transmission  line  towers  on  which  competitive  bids  are  to  be  re- 
ceived. Usually  for  a  line  requiring  several  towers,  the  Engineer  in 
charge  of  the  installation  will  determine  the  arrangement  of  all  the 
wires,  the  limiting  dimensions  for  the  structures,  and  the  loadings  for 
them;  but  the  design  of  the  structures  will  be  left  generally  to  the 
Manufacturer,  subject,  however,  to  those  provisions  of  the  specifica- 
tions which  are  intended  to  insure  that  the  towers  or  poles  will  all  be 
designed  to  have  the  same  strength.  Different  Engineers  seek  to 
accomplish  this  result  in  as  many  different  ways.  Some  will  specify 
the  loadings  under  which  they  expect  the  towers  to  be  used,  and  will 
stipulate  that  the  design  shall  provide  sufficient  strength  to  take  care 
of  these  loadings  with  a  given  factor  of  safety;  others  wi'.l  state  unit 
stresses  which  shall  be  used  in  determining  the  sections  in  the  design, 
to  take  care  of  the  stresses  resulting  from  the  above  loadings.  Other 
Engineers  will  increase  the  desired  working  loads  by  some  factor  which 
they  will  introduce  as  a  margin  of  safety,  and  will  then  give  these  in- 
creased loadings  instead  of  the  working  loadings,  and  will  require  that 
the  structures  be  designed  to  withstand  these  loadings  without  failure. 
Still  other  Engineers  will  specify  that  certain  unit  stresses  shall  be  used 
in  determining  a  design,  which  shall  support  the  specified  loadings  with 
a  given  factor  of  safety;  and,  further,  that  the  completed  structure 
must  support  loads  that  are  twice  as  large  as  those  specified,  but  with- 
out any  restriction  regarding  unit  stresses  to  be  employed. 

FACTOR  OF  SAFETY 

The  term  "Factor  of  Safety"  is  in  reality  a  misnomer,  and,  because 
of  this,  it  is  not  always  interpreted  in  the  same  way  by  different  men. 
Literally  speaking,  the  structure  which  is  properly  designed  with  a 
factor  of  safety  of  three,  should  sustain  without  failure  loads  three 
times  as  great  as  those  which  are  expected  to  be  the  working  loads 
under  normal  conditions.  But  the  term  "Factor  of  Safety,"  as  it  is 
usually  interpreted  and  applied,  means  that  the  unit  stresses  used 
throughout  shall  be  one-third  the  ultimate  strength  of  the  material 
entering  into  the  construction.  In  actual  practice  the  results  of  such 
an  interpretation  are  very  disappointing.  In  a  composite  structure 


Transmission  Towers  43 

made  up  of  a  large  number  of  different  pieces,  some  of  which  are  under- 
going compression  while  others  are  in  tension,  the  action  of  this  body 
as  a  whole  against  outside  forces  will  differ  radically  from  what  would 
be  expected  of  any  one  of  its  component  parts  under  a  similar  test. 
This,  of  course,  is  accentuated  in  the  case  of  transmission  towers, 
because  they  are  always  made  as  light  as  possible  for  the  work  required 
of  them,  and,  hence  when  under  load,  they  deflect  considerably  from 
their  original  outlines,  and  this  in  turn  produces  a  rearrangement  and 
entirely  different  distribution  of  stresses.  The  net  result  of  all  this  is, 
that  all  such  structures  will  fail  when  the  loading  on  them  reaches  the 
point  where  some,  if  not  all,  of  the  members  making  up  the  construc- 
tion are  stressed  to  the  elastic  limit  for  their  material. 

Since  the  elastic  limit  for  steel  in  either  tension  or  compression  is 
about  one-half  its  ultimate  strength,  it  follows  that  the  structure  whose 
members  are  determined  by  using  unit  stresses  equal  to  one-third  of 
the  ultimate  strength  of  the  material,  will  have  a  total  strength  only 
50%  in  excess  of  that  required  to  take  care  of  actual  working  condi- 
tions; so  that,  instead  of  having  the  so-called  "Factor  of  Safety  of 
Three"  it  has  an  actual  factor  of  safety  of  one  and  one-half. 

This  fact  is  recognized  by  those  who  first  multiply  the  required  work- 
ing loads  by  a  factor  which  will  provide  a  margin  of  safety,  and  then 
specify  that  the  towers  shall  support  without  failure  these  increased 
stipulated  loads.  It  is  not  often  that,  under  these  conditions,  the 
specifications  will  call  for  the  employment  of  definite  unit  stresses  in 
determining  the  several  sections  of  material  to  be  used.  But  in  all 
such  cases,  when  unit  stresses  are  specified,  it  will  almost  always  be 
found  that  those  recommended  are  close  to  the  elastic  limit  for  the 
material. 

UNIT  STRESSES 

The  unit  stress  for  a  member  in  either  tension  or  compression  is  the 
quotient  of  the  total  load  divided  by  the  cross  sectional  area  of  the 
member  supporting  the  load.  This  is  given  in  pounds  per  square  inch. 
The  unit  stress  for  a  member  in  compression  is  less  than  that  for  a 
member  in  tension  by  a  quantity  which  is  a  function  of  the  ratio 
between  the  unsupported  length  of  the  member  and  its  least  radius 
of  gyration.  Usually  this  unit  stress  is  determined  by  a  straight-line 
formula,  such  as 


44  Transmission  Towers 

Sc    =  S  —  C  —  in  which 

K 

Sc  =  the  desired  unit  stress  in  compression, 

S  =  the  unit  stress  allowed  in  tension, 

L  =  the  unsupported  length  of  the  member  in  inches, 

R  =  the  least  radius  of  gyration  for  the  member,  in  inches, 

C  =  a  constant  determined  by  experimental  investigation. 

The  elastic  limit  in  tension  is  about  27000  pounds  per  square  inch  of 

net  section.     The  straight-line  formula  27000  —  90  =r  for  unit  stresses 

R 

in  compression,  gives  values  which  have  been  proven  by  actual  tests 
to  be  approximately  the  elastic  limit  for  the  material. 

Where  the  so-called  ' 'Factor  of  Safety  of  Three"  is  wanted,  the  unit 
stress  generally  specified  for  members  in  tension  is  18000  pounds  per 
square  inch  of  net  section,  while,  for  unit  stress  for  members  in  com- 
pression, the  formula 

18000  —  60  £  is  specified. 
K 

It  will  be  noted  that  these  values  are  just  two- thirds  of  those  im- 
mediately preceding,  and,  therefore,  offer  a  margin  of  safety  of  50%. 
It  is  not  often  that  unit  stresses  smaller  than  these  are  specified  for 
tower  work,  but  occasionally  we  find  specifications  which  are  very 
severe,  considering  the  infrequency  of  maximum  or  even  full  loads  on 
this  type  of  structure. 

It  is  common  practice  among  Engineers,  when  specifying  that  the 
towers  shall  safely  support  certain  loads,  to  refrain  from  putting  any 
limitations  on  the  design,  such  as  what  relationship  shall  be  allowed  as 
a  maximum  between  the  length  of  any  compression  member  and  its 
least  radius  of  gyration.  On  the  other  hand,  when  it  is  stipulated  that 
the  structures  shall  be  figured  for  carrying  certain  loads  by  using  given 
unit  stresses,  it  is  almost  always  also  stipulated  that  the  ratio  of  length 
of  compression  members  to  their  least  radius  of  gyration  shall  be 
limited  to  a  certain  maximum  value. 

BOLT  VALUES 

Bolts  stressed  to  24000  pounds  per  square  inch  in  shear  have  value* 
comparable  with  the  strength  of  members  which  are  figured  on  the 
basis  of  27000  pounds  per  square  inch  of  net  section  in  tension,  or  27000 


Transmission  Towers  45 

L 

-  90  •=?  pounds  per  square  inch  of  gross  section  in  compression.     From 

IN. 

this  it  follows  that  bolts  need  not  be  stressed  lower  than  16000  pounds 
per  square  inch  in  shear  to  get  values  corresponding  to  those  resulting 
from  using  18000  pounds  per  square  inch  of  net  section  in  tension  or 

18000  —  60  TT  pounds  per  square  inch  of  gross  section  in  compression, 
K. 

for  members  which  are  to  be  connected  by  means  of  these  bolts.  It  is 
evident  that  smaller  values  for  bolts  are  unwarranted.  Consistent 
practice  in  designing  requires  that  the  values  assumed  for  bolts  shall 
bear  the  same  ratio  to  their  elastic  limit  as  the  ratio  obtaining  between 
the  working  value  assumed  and  the  elastic  limit  for  the  several  mem- 
bers which  are  connected  by  the  bolts. 

LOADINGS 

In  regard  to  the  specific  loadings  for  which  the  structures  shall  be 
designed,  considerable  depends  upon  where  they  are  to  be  used,  as 
there  are  several  factors  entering  into  this  question. 

The  first  thing  that  should  be  determined  is  the  kind  and  maximum 
value  of  the  vertical  load  to  be  taken  care  of  at  the  end  of  the  cross  arm. 
If  the  line  runs  through  a  comparatively  level  country,  there  is  no 
reason  why  there  should  ever  be  any  uplift  at  the  end  of  the  cross  arm ; 
but  if  the  line  runs  along  steep  grades,  then  there  may  be  times  when 
the  vertical  load  will  be  upward  rather  than  downward.  This  is  of 
considerable  consequence  in  the  designing  of  the  tower.  The  vertical 
load  at  the  end  of  the  cross  arm  is  usually  supported  by  members 
which  run  from  the  end  of  the  cross  arm  to  the  main  post  angles  at 
some  point  above  the  cross  arm.  If  the  vertical  load  is  downward, 
these  supporting  members  will  act  in  tension,  but  if  the  load  can  ever 
be  upward  instead  of  downward,  then,  such  members  must  be  capable 
of  taking  stress  in  compression.  In  cases  where  the  cross  arms  are 
long,  which  is  almost  always  true  when  suspension  insulators  are  used, 
these  members  must  be  made  much  heavier  to  take  the  stress  in  com- 
pression, rather  than  tension. 

ANGLE  TOWERS 

The  next  thing  to  determine,  if  possible,  is,  how  many  towers  will 
have  to  take  care  of  angles  in  the  line,  and  what  will  be  the  maximum 
angle  encountered.  If  this  angle  should  be  very  large,  it  will  be  neces- 


46  Transmission  Towers 

sary  to  provide  special  structures  for  such  points  in  the  line;  but  if  the 
angle  is  very  small,  provision  for  it  may  be  made  by  using  one  of  the 
straight  line  towers  at  this  point  and  shortening  the  span  on  each  side 
of  it.  This  shortening  of  the  span  reduces  the  wind  load  on  the  wires 
transverse  to  the  direction  of  the  line,  and  at  the  same  time  reduces  the 
pull  in  the  wires  in  the  direction  of  the  line,  if  the  sag  is  made  a  greater 
percentage  of  the  shortened  span  than  it  is  in  the  case  of  the  adjoining 
spans. 

In  Fig.  11  there  is  shown  a  graphical  diagram  of  the  components  of 
the  tension  in  the  wire,  parallel  to  the  faces  of  the  tower,  when  its  axis 
parallel  to  the  cross  arm  bisects  the  given  angle  in  the  line.  It  will  be 
seen  that  when  the  wires  leading  off  in  both  directions  from  the  end  of 
the  cross  arm  have  equal  stresses,  the  component  "Y"  in  one  wire 
balances  the  corresponding  component  from  the  other  wire,  but  that 
the  component  "X"  is  twice  what  it  is  when  only  one  wire  leads  off 
from  the  cross  arm.  This  means  that  in  the  one  case,  marked  condi- 
tion "B,"  the  load  on  the  tower  is  twice  the  component  "X"  from  one 
wire,  but  that  for  condition  "A,"  the  load  on  the  tower  is  the  sum  of  the 
components  "Y"  and  "X"  from  one  wire. 

It  will  be  noted  that  for  condition  "B"  the  total  load  on  the  tower 
from  the  pull  in  the  direction  of  the  line  will  just  equal  this  pull  when 
the  tower  bisects  an  angle  of  sixty  degrees  in  the  line,  and  that  this  load 
increases  to  double  the  pull  on  one  wire,  as  a  maximum  limit,  when  the 
angle  in  the  line  reaches  one  hundred  eighty  degrees.  For  condition 
"A"  the  total  load  will  always  be  greater  than  the  pull  in  the  wire,  no 
matter  how  small  the  angle  in  the  line,  and  the  worst  loading  will  occur 
when  the  tower  bisects  an  angle  of  ninety  degrees  in  the  line.  When 
the  angle  in  the  line  is  as  large  as  ninety  degrees,  it  will  often  be  more 
desirable  to  construct  a  special  tower,  and  to  set  it  normal  to  the  direc- 
tion of  the  line. 

SPECIAL  TOWERS 

Having  determined  whether  it  will  be  necessary  to  provide  special 
towers  to  take  care  of  angles  in  the  line,  the  next  step  should  be  to 
determine  how  many,  if  any,  special  towers  should  be  provided  to  take 
care  of  such  special  cases  as  railroad  crossings,  and  what  specifications 
must  govern  in  the  design  of  these  special  structures.  The  Railroad 
Companies  have  their  own  specifications  for  these  structures,  and  they 


Transmission  Towers 


47 


Value  of  COMPONENT   Y  fir  tension  of  1000  Ib.  in  win 
(tor  Condition  A.    For  Condition  B  the  components  balance  and  their  sum  'a  zero) 


TRANSVEBX  AHD  Lff  COMPONENTS 

ANGLE  TOWERS 

B/sfcr  THf  AHGLC  IH  THE  LINE 


too       too        ioo4ooxo60oioo6oo9oo        1000  (Condition  A] 

tOO         *W  tOO         800         IOOO        ItOO         MOO         I6OO        1800          tOOO  / 

Value  of  COMPONENT  X  for  tension  of  IOOO  Ik  in  wire. 


Fi*.  11 


48  Transmission  Towers 

insist  that  all  wires  carried  over  their  crossings  shall  be  supported  by 
structures  complying  with  all  their  requirements  as  to  loadings  and  unit 
stresses  to  be  employed.  Their  specifications  are  generally  very  severe 
and,  hence,  special  designs  almost  always  are  required  for  those 
particular  points  in  the  line.  Of  course,  one  thing  always  to  be  kept 
in  mind,  is  to  make  as  few  different  designs  as  circumstances  will  allow, 
so  that  there  will  be  as  much  duplication  as  possible  in  the  structures. 
This  is  an  especial  advantage  for  economical  fabrication  in  the  shop, 
and  is  also  a  big  advantage  when  it  comes  to  erecting  the  towers  in  the 
field. 

Every  line  must  be  carefully  studied  and  designed  for  its  own 
particular  requirements.  A  line  wrhich  is  taken  through  a  city  must  be 
built  in  a  different  way  from  one  going  through  an  open  country.  The 
working  loads  might  not  need  to  be  any  heavier,  but  either  the  design 
loads  should  be  heavier  or  the  unit  stresses  lower,  and  the  towers 
should  be  spaced  closer  together. 

REGULAR  LINE  TOWERS 

The  average  line  of  any  length  should  have  three  different  types  of 
towers.  These  may  be  designated  as — Standard  or  Straight  Line, 
Anchor,  and  Dead  End  Towers. 

All  towers  should  be  designed  to  take  care  of  the  dead  weight  of  the 
structures  and  also  the  vertical  loads  at  the  ends  of  all  the  cross  arms, 
in  addition  to  and  simultaneously  with,  the  horizontal  loadings  speci- 
fied below. 

• 

STANDARD  TOWERS 

The  Standard,  or  Straight  Line,  Towers  should  predominate,  and 
should  be  designed  to  support  without  failure  the  required  horizontal 
loads  transverse  to  the  direction  of  the  line,  combined  with  a  horizontal 
pull  in  the  direction  of  the  line  applied  at  any  one  insulator  connec- 
tion equivalent  to  the  value  of  the  wire  when  stressed  to  about  one-half 
its  ultimate  strength.  These  loads  transverse  to  the  line  should  be 
large  enough  to  include  the  wind  load  across  the  wires  and  that  against 
the  tower  itself,  with  a  little  margin  of  safety. 

ANCHOR  TOWERS 

The  Anchor  Tower  should  be  designed  to  support  without  failure 
any  one  of  the  following  horizontal  loadings: 


Transmission  Towers  49 

(1)  The  same  horizontal  loads  as  those  specified  for  the  Standard 
Tower. 

(2)  An  unbalanced  horizontal  pull  in  the  direction  of  the  line  equiva- 
lent to  the  working  loads  of  all  the  conductor  wires  and  the  ground 
wires,  applied  at  the  points  of  connection  of  the  wires  to  the  tower, 
combined  with  the  transverse  horizontal  loads  on  the  wires  and  the 
tower. 

(3)  An  unbalanced  horizontal  pull  parallel  to  the  line  equivalent  to 
the  working  loads  of  the  wires,  applied  at  one  end  of  each  cross  arm, 
all  on  the  same  side  of  the  tower  and  all  acting  in  the  same  direction, 
combined  with  the  horizontal  transverse  loads  on  the  wires  and  the 
tower. 

DEAD  END  TOWERS 

The  Dead  End  Towers  should  be  designed  to  support  the  same  load- 
ings as  those  specified  for  the  Anchor  Towers,  but  the  sections  should 
be  determined  by  using  smaller  unit  stresses.  Unit  stresses  of  18000 

pounds  per  sq.  in.  in  tension  and  18000  —  60  -=r  for  compression,  would 

give  these  towers  approximately  50%  more  strength  than  the  anchor 
towers  would  have  when  stressed  just  within  the  elastic  limit. 

It  will  be  noted  that  under  the  above  specification,  the  standard 
tower  will  be  required  to  take  care  of  the  torque  resulting  from  an  un- 
balanced horizontal  pull  equivalent  to  the  allowable  tension  (which 
is  one-half  the  ultimate  strength)  of  one  wire,  applied  at  one  end  of  any 
cross  arm  and  acting  parallel  to  the. direction  of  the  line;  while,  the 
anchor  and  the  dead  end  towers  are  both  required  to  take  care  of  either 
the  torque  as  given  above  for  the  standard  tower  or  the  torque  result- 
ing from  an  unbalanced  horizontal  pull  equivalent  to  the  working 
loads  (actual  tension  in  the  wire  under  the  working  conditions)  of  all 
the  wires  on  either  side  of  the  center  line  of  the  tower,  applied  at  one 
end  of  each  of  the  cross  arms,  and  all  acting  parallel  to  the  line  and  in 
the  same  direction.  If  one  anchor  tower  is  placed  in  the  line  for  every 
ten  or  twelve  standard  towers,  all  conditions  resulting  from  broken 
conductor  wires  should  be  localized  to  the  territory  between  two  an- 
chor towers.  The  reason  for  using  lower  unit  stresses  in  the  dead  end 
towers  than  in  the  anchor  towers  for  exactly  the  same  loadings,  is  that 
the  dead  end  towers  may  have  to  support  a  large  part  of  this  total  load- 
ing at  all  times,  and  all  of  it  very  frequently,  while  the  anchor  tower 


50  Transmission  Towers 

may  have  to  support  the  same  loading  only  once  in  a  great  while,  and 
then  for  only  a  very  brief  time. 

One  of  the  aims  to  be  kept  constantly  in  mind  in  designing  a  trans- 
mission structure,  is  to  get  a  finished  tower  in  which  all  the  stresses  can 
be  determined  definitely.  We  usually  determine  the  stresses  graphic- 
ally. The  stresses  resulting  from  the  horizontal  loads  applied  as  so 
much  shear  must  be  determined  separately  from  the  stresses  resulting 
from  torque.  These  stress  diagrams  cannot  be  combined  except  in 
those  cases  where  the  slope  of  the  post  does  not  change  between  the 
horizontal  planes  bounding  that  part  of  the  tower  for  which  the  dia- 
grams are  wanted.  This  is  true  because  the  horizontal  loads  which  act 
as  so  much  shear,  may  be  assumed  to  be  acting  in  a  plane  containing 
both  posts  of  the  face  of  the  tower,  parallel  to  the  direction  of  the  load, 
in  which  case  the  posts  may  or  may  not  (depending  upon  the  slope  of 
the  posts)  take  up  a  part  of  this  shear  directly.  On  the  other  hand, 
the  torque  is  a  moment  acting  in  a  horizontal  plane  and  is  constant 
between  any  two  parallel  planes,  unless  it  is  either  increased  or  de- 
creased by  an  additional  torque  of  the  same  or  opposite  kind. 

ANCHORAGE  DESIGNS 

The  members  for  anchoring  the  structure  to  the  footings  are  gener- 
ally the  last  part  of  the  design  to  be  considered. 

The  first  question  to  be  determined  is  whether  concrete  footings  shall 
be  used.  These  are  more  simple,  and  involve  much  less  steel  work 
than  any  other  type  of  footing  used  for  transmission  line  structures. 
The  weight  of  the  concrete  itself  reacts  against  the  tendency  of  the  post 
to  pull  away  from  the  base  because  of  the  tension  in  the  post  on  one 
side  of  the  tower.  It  also  offers  more  bearing  surface  against  the  earth 
around  the  footings  and  introduces  the  passive  resistance  of  a  larger 
volume  of  earth  against  the  uplifting  tendency  of  the  post  on  the  ten- 
sion side  of  the  tower.  Of  course,  the  saving  in  the  cost  of  steel  in  the 
structure  must  be  balanced  against  the  expense  involved  in  putting 
the  concrete  in  place,  to  determine  whether  or  not  it  is  advisable  to 
use  concrete  footings.  This  will  depend  upon  many  circumstances 
which  must  be  very  carefully  considered  before  reaching  a  conclusion. 
It  is  impossible  to  overestimate  the  importance  of  good  anchorages. 
An  otherwise  excellent  construction  may  be  made  inadequate  by  using 
footings  which  are  not  substantial.  If  one  of  the  footings  should  be 


Transmission  Towers 


5plice  ang/e 


Concrete  —- 


Anchor  bolts, 
40to50diam. 
in  concrete 


Concrete  Anchors 


Concrete  pad- 


Anchor 

grouted  in  drilled  holes. 


Rock  Anchor 


Splice  angk^&  Ground  line^ 


Earth  Anchor 


Fiji.  12 


52  Transmission  Towers 

insufficient  to  take  care  of  the  loads  for  which  the  superstructure  is 
intended,  it  would  be  very  apt  to  yield  under  full  loading,  and,  in  doing 
so,  would  bring  about  a  new  distribution  of  stresses  among  the  mem- 
bers, and  would  put  on  some  of  the  members  stresses  which  were  not  in 
keeping  with  those  for  which  the  members  were  designed.  Such  a  re- 
arrangement of  stresses  may  very  easily  be  so  vital  as  to  bring  about 
the  failure  of  the  superstructure.  In  view  of  this  fact,  it  is  recom- 
mended that,  where  there  is  any  doubt  as  to  whether  concrete  footings 
should  be  used,  the  benefit  of  any  small  doubt  should  always  be  given 
in  favor  of  such  footings.  But,  it  may  be  that  the  structures  are  to  be 
used  where  such  footings  would  be  practically  impossible.  Under  such 
circumstances,  other  provisions  must,  of  course,  be  made. 

In  the  case  of  poles,  the  regular  outline  is  generally  continued  below 
thie  surface  of  the  ground  whether  concrete  footings  are  used  or  not; 
but  if  concrete  is  not  used,  then  additional  steel  must  almost  always 
be  used  to  get  more  bearing  area  against  the  earth. 

In  the  case  of  towers  there  is  provided  a  separate  footing  for  each  of 
the  posts.  When  concrete  footings  are  used  the  posts  are  connected 
to  them  in  one  of  two  ways:  In  the  first  method,  extensions  of  the  post 
sections,  which  are  called  anchor  stubs,  may  be  built  in  these  footings 
with  just  sufficient  length  extending  above  the  concrete  so  that  the 
lower  post  sections  of  the  tower  may  be  connected  directly  to  them. 
These  anchor  stubs  may  extend  almost  to  the  bottom  of  the  footing,  or 
they  may  extend  into  the  footings  only  far  enough  that  the  adhesion  of 
the  concrete  to  them  will  develop  their  full  strength,  in  which  case  it 
will  be  necessary  to  add  steel  reinforcing  bars  from  this  point  to  the 
bottom  of  the  concrete.  This  is  necessary  because  provision  must  be 
made  to  bind  the  concrete  together  so  that  it  will  not  break  apart 
under  the  uplifting  force  in  the  post,  and  thus  defeat  its  purpose.  The 
other  method  used  with  the  concrete  footing  is  to  have  a  base  at  the 
lower  end  of  the  post  section  which  will  bear  directly  on  the  mass  of 
concrete  in  the  footing,  and  which  will  at  the  same  time  be  connected 
directly  to  this  concrete  by  means  of  long  bolts  or  rods  extending  well 
into  the  mass  of  concrete.  These  rods,  in  this  case,  would  be  brought 
into  action  only  when  the  post  is  under  tension.  If  these  rods  are 
straight  for  their  full  length,  and  fairly  large,  they  should  be  imbedded 
in  the  concrete  for  a  length  equal  to  fifty  times  their  diameter,  in  order 
to  develop  their  full  breaking  strength.  But  if  these  rods  are  bent  a 
little  near  their  lower  ends,  their  breaking  strength  will  be  developed 


Transmission  Towers  53 

by  imbedding  them  in  the  concrete  for  a  length  equal  to  forty  times 
their  diameter.  Provision  for  binding  together  the  concrete  in  the 
footing  must  be  made  when  anchor  rods  are  employed,  just  the  same 
as  when  anchor  stubs  are  used. 

With  any  type  of  footing,  there  must  be  provided  sufficient  bearing 
surface  against  the  earth  to  resist  the  maximum  compression  in  the 
post,  and  also  an  arrangement  to  lift  enough  earth  to  resist  the  maxi- 
mum uplifting  tendency  in  the  post  under  the  worst  condition  of 
loading. 

The  most  positive  and  direct  way  to  determine  the  size  and  outline 
of  a  footing  for  any  given  loading,  is  to  increase  this  loading  by  the 
desired  factor  of  safety,  and  then  to  determine  a  footing  of  which  the 
ultimate  resisting  value  will  be  sufficient  to  meet  the  conditions  to  be 
imposed.  We  recommend  that  the  footing  be  so  designed  that  its 
ultimate  resisting  value  will  be  not  less  than  25%  in  excess  of  what  is 
necessary  to  sustain  the  loading  specified  for  the  pole  or  tower. 

For  specially  heavy  towers  which  are  required  to  dead-end  heavy 
wires  on  long  spans,  it  sometimes  becomes  a  troublesome  matter  to 
provide  adequate  footings  to  take  care  of  the  uplift  from  the  posts  on 
the  tension  side  of  the  tower  under  the  assumed  condition  of  maximum 
loading.  This  often  happens  in  the  case  of  ^River-Crossing  Towers. 
Footings  for  such  cases,  if  built  in  the  ordinary  way,  would  have  to  be 
made  very  deep  and  would  require  a  large  amount  of  concrete.  It  will 
often  be  found  to  be  economical  to  design  these  footings  with  special 
outline  and  construction. 

The  following  rather  unique  method  has  been  successfully  employed 
for  taking  care  of  cases  involving  unusually  large  uplifts,  when  the 
footings  are  built  in  clay  or  in  mixed  clay  and  sand  that  is  compara- 
tively free  of  gravel.  A  square  pit  is  dug  deep  enough  that  its  bottom 
will  be  below  the  frost  line  and  large  enough  to  afford  sufficient  bearing 
area  against  earth  to  sustain  any  possible  downward  pressure  where 
the  tower  post  may  be  subjected  to  either  tension  or  compression.  In 
the  center  of  this  pit  a  hole  about  twenty  inches  in  diameter  is  bored 
with  an  earth-auger  to  the  depth  desired  (this  depth  has  been  made  as 
much  as  twenty  feet  below  the  bottom  of  the  square  pit).  Dynamite 
is  then  placed  in  the  bottom  of  this  hole  and  connected  with  a  firing 
magneto;  then  the  hole  is  filled  with  concrete  of  1 :2 :4  mixture,  medium 
wet,  and  the  charge  of  dynamite  is  fired  immediately.  The  charge  of 
dynamite  that  is  generally  used  for  this  purpose  consists  of  eight  one- 


54  Transmission  Towers 

half  pound  sticks  of  60%  dynamite.  Reinforcing  bars  with  their  ends 
bent  are  then  pushed  down  through  the  concrete  to  the  bottom  of  the 
hole  and  then  raised  three  inches  and  securely  held  in  this  position  to 
prevent  them  from  sinking  through  the  concrete  and  coming  in  con- 
tact with  the  earth  before  the  concrete  has  set.  The  hole  is  then  re- 
filled with  concrete,  and  the  footing  in  the  square  pit  is  also  poured  and 
finished.  From  the  moment  the  dynamite  is  placed  and  connected 
with  the  firing  magneto,  it  is  essential  that  all  the  subsequent  opera- 
tions be  conducted  as  rapidly  as  possible.  Not  more  than  five  minutes 
should  be  allowed  between  the  time  when  the  first  pouring  of  concrete 
is  started  and  when  the  dynamite  is  fired. 

The  average  displacement  from  such  an  explosion  of  dynamite  is 
about  one  and  one-half  cubic  yards,  this,  of  course,  being  dependent 
upon  the  depth  of  the  hole  and  the  nature  of  the  surrounding  earth. 
Experimental  footings  placed  in  this  manner  show  that  the  enlarged 
base  takes  an  almost  spherical  form  with  its  center  above  the  bottom  of 
the  excavated  hole  a  distance  equal  to  about  one-fourth  the  horizontal 
diameter  of  the  enlarged  base.  This  diameter  is  sometimes  almost  four 
feet.  It  is  evident  that  a  footing  of  this  kind  can  be  made  to  resist  a 
very  large  uplifting  pull. 

In  the  case  of  light  towers  it  is  sometimes  considered  advisable  to  put 
the  tower  in  its  erect  position  above  the  ground  before  the  anchors  are 
set,  and  to  then  bolt  these  footing  members  to  the  lower  end  of  the  main 
tower  legs  and  put  concrete  or  earth  back  fill  around  them  while  the 
tower  is  being  supported  independent  of  them.  But  in  the  case  of 
heavy  towers  it  is  generally  considered  more  economical  to  set  the  foot- 
ing members  exactly  in  their  position  first,  and  to  then  erect  the  towers 
and  connect  them  to  their  footings.  This  latter  method  of  erection 
requires  that  the  anchor  stubs  be  aligned  as  accurately  as  possible,  as 
any  inaccuracy  in  the  setting  of  these  anchors  will  make  the  subsequent 
assembling  of  the  tower  more  difficult  and  less  satisfactory.  If  the 
anchor  stubs  are  not  set  accurately  to  their  true  positions,  there  will  be 
introduced  in  the  tower,  additional  stresses  for  which  the  tower  mem- 
bers were  not  designed.  An  accurate  alignment  of  the  anchors  can  be 
accomplished  only  by  using  rigid  templates  that  will  hold  the  anchors 
in  their  definite  positions  until  they  have  been  secured  by  either  the 
back  fill  or  concrete. 

Almost  all  towers  are  built  smaller  at  the  top  than  at  the  ground 
line,  and  the  tower  leg  inclines  from  the  vertical  as  determined  by  this 


Transmission  Towers 


55 


outline  of  the  structure.  The  anchor  stub  generally  follows  the. direc- 
tion of  the  main  tower  leg,  but  when  it  is  put  in  this  position  and  sus- 
pended from  a  template  it  has  a 
tendency  to  swing  to  the  vertical 
position.  To  obviate  this  condi- 
tion the  setting  template  should 
be  trussed  as  shown  in  Fig.  13. 


TCMPLATT 

fOK 

ANCHORS 


•  aoft  pests  art  ^•^•^L 


Fig.  13 


ERECTION 

Transmission  towers  are 
erected  in  one  of  two  ways:  they 
may  be  erected  by  assembling 
the  members  one  at  a  time  in 
their  proper  positions  in  the  com- 
pleted structure,  or  by  assemb- 
ling the  complete  structure  in  a 
prone  position,  and  raising  it  to  its  vertical  position  by  swinging  it 
about  two  hinge  points  on  or  near  two  anchor  stubs. 

If  the  first  of  these  two  methods  is  used,  there  will  generally  be  re- 
quired a  crew  of  eight  men,  including  one  foreman.  The  following 
equipment  will  generally  suffice: 

One  light  gin-pole,  about  25  feet  long. 

One  set  of  two-sheave  and  three-sheave  blocks  for  %  *  diameter  rope. 
About  300  feet  of  %"  diameter  rope;   four  hand  lines,  each  about 
150  feet  long;  four  small  gate  blocks  for  the  hand  lines. 

The  post  members  are  erected  with  the  gin-pole  and  tackle,  but  all 
the  other  members  are  pulled  up  from  the  ground  with  the  hand  lines. 
The  time  required  will  be  about  the  same  whether  the  tower  is  light  or 
heavy.  The  time  required  will,  however,  depend  upon  both  the 
accuracy  of  the  fabrication  of  the  material  and  the  accuracy  of  the 
alignment  of  the  anchor  stubs. 

If  the  second  method  is  used,  the  actual  work  erecting  the  tower  does 
not  consume  more  than  ten  or  fifteen  minutes  after  all  the  prepara- 
tions have  been  made.  These  preparations  and  the  erection  consist  of 
three  distinct  operations: 

(1)  Leveling  the  ground  where  required  for  the  erection 
equipment,  and  blocking  up  the  tower  on  rough  ground 
and  for  side-hill  extensions.  A  crew  of  seven  or  nine 
men  including  a  foreman  is  required. 


56  Transmission  Towers 

(2)  Rigging   up   erection   equipment,   and   bolting  erection 

shoes  and  struts  in  place,  etc.  A  crew  of  about  twelve 
men  including  a  foreman  is  required. 

(3)  The  actual  raising  of  the  tower.     Sometimes  horses  are 

used  for  this  operation,  but  it  is  often  found  to  be  more 
satisfactory  to  use  a  caterpillar  tractor,  especially  for 
raising  the  heavier  towers.  One  team  of  horses  will 
generally  suffice  for  this  work,  but  it  often  requires  four 
and  sometimes  six  horses  especially  in  rough  country 
and  for  raising  towers  that  are  unusually  heavy.  The 
Tractor  gives  a  much  steadier  pull,  and  will  permit  of 
holding  the  load  at  any  desired  point  more  satisfac- 
torily than  when  horses  are  used.  A  substantial  A-- 
frame usually  built  up  of  steel  pipes  is  generally  em- 
ployed for  raising  the  tower  from  the  prone  to  the  up- 
right position.  A  steel  cable  should  also  be  used  in 
preference  to  a  manilla  rope  for  this  purpose  in  the  case 
of  the  heavier  towers. 

When  concrete  footings  are  used,  and  this  method  of  erection  is  em- 
ployed, there  is  an  advantage  in  having  the  anchor  stubs  set  and  con- 
creted in  position  in  advance  of  the  assembling  of  the  tower.  When 
this  is  done,  the  tower  can  be  assembled  close  to  the  anchor  stub  and 
can  be  raised  about  hinges  fastened  to  the  tops  of  the  anchor  stubs; 
but  when  the  tower  is  assembled  before  the  concrete  is  placed  around 
the  anchor  stubs,  it  is  necessary  to  assemble  the  tower  a  few  feet  away 
from  the  stubs,  and  then  to  skid  the  tower  into  the  position  from  which 
it  is  to  be  raised.  This  process  of  skidding  the  tower  is  costly,  and  is 
also  likely  to  injure  the  tower  members. 

SPACING  OF  TOWERS 

The  trend  of  American  practice  today  in  the  designing  of  transmis- 
sion line  installations  is  to  make  the  spans  between  supporting  struc- 
tures as  great  as  possible.  As  the  result  of  considerable  study  extend- 
ing over  several  years  of  experience  with  lines  having  spans  some  of 
which  were  very  short  while  others  were  exceptionally  long,  it  has  been 
determined  that  the  best  and  most  economical  lines,  all  things  con- 
sidered, are  those  in  which  the  supporting  structures  are  spaced 
far  apart. 


Transmission  Towers  57 

This  is  true  even  though  the  first  investment  for  the  original  installa- 
tion is  somewhat  larger  in  the  case  of  long  spans  than  where  short 
spans  are  used.  It  has  been  determined  from  comparative  records 
that  the  maintenance  of  lines  having  the  long  spans  is  much  less  than 
was  the  maintenance  of  the  same  lines  during  previous  periods  when 
shorter  spans  were  used.  This  decreased  cost  of  maintenance  has 
been  proved  to  be  sufficiently  important  to  warrant  making  larger 
initial  investments  on  original  projects.  The  maintenance  is  not  only 
less  expensive  with  the  long  spans  but  it  is  also  less  troublesome, 
because  there  is  less  interference  with  continuous  service  along  the  line. 
This  is  a  matter  worthy  of  careful  consideration,  as  the  value  of  elec- 
trical service  in  almost  every  case  is  dependent  upon  the  assurance  of 
its  continuity. 

By  using  long  spans  the  number  of  insulators  required  is  reduced; 
and,  as  there  is  always  a  chance  that  a  flash-over  will  occur  at  the 
insulator,  it  is  obviously  advisable  to  reduce  the  number  of  insulators 
to  a  minimum  in  order  to  eliminate,  as  far  as  possible,  this  source  of 
trouble  for  the  service. 

Another  advantage  derived  from  the  use  of  long  spans  is  that  the 
variations  of  stress  in  the  wires  resulting  from  large  changes  in  tem- 
perature will  be  much  less  than  under  similar  conditions  of  loading  on 
short  spans.  The  constant  changing  of  stress  in  the  wires  is  produc- 
tive of  more  trouble  than  higher  stresses  which  are  more  uniformly 
applied. 

The  long  span  is  especially  advantageous  for  a  line  carried  along  a 
hillside,  because  it  will  generally  permit  of  such  an  arrangement  of 
towers  that  there  will  not  be  any  upward  pull  on  any  of  them.  The 
upward  pulls  are  always  a  source  of  trouble,  and  they  should  be  elim- 
inated wherever  conditions  will  permit  an  alternative  construction. 
The  upward  pull  causes  not  only  mechanical  but  also  electrical  troubles, 
because,  during  a  rain  storm,  water  will  run  down  along  the  wire  into 
the  insulator,  which,  of  course,  immediately  produces  electrical  trouble. 

The  voltages  used  on  present  day  high  tension  lines  are  such  that 
the  suspension-type  and  strain-type  insulators  are  rapidly  displacing 
the  pin-type  insulators.  This,  of  course,  means  longer  and  heavier 
cross  arms  and  higher  supporting  structures.  It  is  also  true  that  the 
cost  of  wood  is  steadily  increasing,  and  will  continually  increase  as  the 
wood  becomes  less  plentiful.  These  conditions  when  combined  with 
the  tendency  for  long  span  construction  as  described  above,  mean  that 


58  Transmission  Towers 

the  wood  pole  construction  is  being  rapidly  superseded  by  the  better 
and  more  permanent  steel  tower  construction. 

When  the  Manufacturer  is  expected  to  design  the  structures  for  a 
line  of  any  considerable  length,  he  is  generally  furnished  very  definite 
and  complete  specifications  regarding  loadings  and  unit  stresses;  but 
when  he  is  asked  for  quotations  on  only  a  few  structures,  it  is  not  often 
that  full  and  complete  information  regarding  working  conditions  are 
furnished  him.  Nor  will  this  information  always  be  forthcoming, 
even  when  the  customer  is  requested  to  give  more  definite  data.  As  a 
rule,  a  part  of  the  necessary  information  will  be  furnished  by  the  cus- 
tomer, and  it  becomes  the  task  of  the  Manufacturer  to  complete  the 
design  by  making  his  own  assumptions  regarding  the  missing  data. 

The  customer  will  very  often  profit  financially  by  making  as  com- 
plete as  possible  the  information  he  gives  to  the  Manufacturer,  and  it  is 
always  much  more  satisfactory  to  the  designer  to  know  positively  what 
working  conditions  are  to  determine  the  design. 


Transmission  Towers 


59 


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Transmission  Towers 


61 


ed—  B 


TABLE  3 
re  —  Stran 


MAX.  LOAD  PER 
LIN.  FOOT  PLANE 
OF  RESULTANT 


LIN.  F 
ONTAL 


D  PE 
HOR 


R  LIN. 
RTICAL 


w 

\o  «o~  ic  **  ~r  ~i  *^r  »^r  — *  — *  —* 

OOO^I^J  O   *O    *!•    O  r*l   00    —    O  —  %J«   r~    o 

So    10    •*  •*            -4  10    rs    10  •>   *9   W>   «* 

'S    CM    rs   ro  <»>   "5   "5    *»•  ^t^'^ui  10    u^    10    10 

f-a           p^-^p  G>OO- 
CQ 

U      J              ^i  ci  rvi  <N  ---««-  -  -  _-  -  --bd 

p-  J^  <N  JJ  oo  —  «o 
<  S             oq 

UJ           —  —  —  —  — "  —  bo  dodo  dddd 

fOO^O-  f»OOO  t-t~t^.»^  —   —   'f   Oi 

—  oo«o—  ooor^oo  •*  «-•   oo  O  *f<MOoo 

—  —'—'—  —"  —  —  d  dddd  c  d  d  d 

OO^Ovoo  r-   t>.    O   10  u?Tt'*f*?  t*?c1r1c1 

—  odd  dddd  dddd  dddd 

O\l~—    i/}1^  OJOOO'O  ^f*5CN«^  *-^OO^O^ 

<N     fN     fN     f>3  'S     fS     —     — !  —     r-.'     —'     —  —     —     OO 

rs?N  —  —  —  —  —  —  dddd  dddd 

u^dOOC  iOfS>O<*5  vOCSU-!ro  O    t^    —    O 

—  _;^^  dddd  dddd  dddd 

« « _.    |||g  §111  g|S§  iSil 

.«         S§§8  §8§S  S§SS  S8§8 

S                  t^.\O^}«fS  •—    ^OO>  —    in    O>    «O 

—  £                  —    O*  OT  00  rC  10    W)    ro"  r»f 

OOOO  OOOO  OOOO  OOO»n 

T   —    O    O  o^r^—  i^i--.^J<f»5  oOt^OfT) 

D  E  £  J             <^"  —    00   >C  W<   —    oT  I>T  <o"  •*   «*5"  CO  «N    —    —    — 

O^to^^r^-  cocKOfO  060*010  ^*f*i^^ 

fOfjfotN  (N  —  —  —  —  qqq  qqqq 

dddd  dddd  dddd  dodo" 

dddd  o'ddd  do"  do"  dddd 

o  >o  o  »•>  o  "> 


62 


Transmission  Towers 


•**       oo  io  io  ro        CM"  i~»" 

O\  00    CM    ON    ON  «-<     •* 

ON  l^     NO     Tj«    CO  fO     CM 


8    8 


222"33 

°s°;?0*S 


£  2  S 


ON    2-    ?0    ^f 

ri«  io  io  >o 


MAX.  LOAD  PER 
LIN.  FOOT  PLANE 
OF  RESULTANT 


u 

U 


CM    1O    1^-    tf) 

fN    O   f«:    ro 
10    fO     CN    — 


2  q  q  ON      ON  ON 
— '  ^  -,4  d      do 


^   ro    eo    CM 

o  o  o  o 


LIN.  F 
ONTAL 


AD  P 
HO 


3*6* 


O*   «*5 
O    l^ 


o  ^  >o  t^ 

•*    •"    00    VO 
VO    NO    IO    10 


gfgg 

dodo 


o  oo  o  to  oo  >o 

NO    fO     CM    O  CO    t^» 

oo  oo  oo  oo  !•>•  t>. 

dodo  do 


10  r-i  »o  o 
t^  ^H  in  o 

•O    «O    't    •"*• 

6600 


CM  CM  t-^  IO  1-^  CO 

NO  CM  OO  IO  CM  O 

"5  PO  CM  CM  CM  CM 

d  d  d  d  do 


" 


CM    Tt<   r^    —         NO   co 
CM    ~    O    O          ON    ON 

~  •**  «'  ~'      do 


00    •*  O  «*5 

f^    (^  5?  pr, 

«N    O  ON  00 

•4  «N  d  e 


«^-    NO    NO    IO         IO    't 

d  d  d  d      do 


•*  O  O  <^J 
«.  "J  •*.  ^ 
0000 


CO  CM  0>  NO  O     0> 

»O  O  IO  fN  O    t^ 

CM  CM  ~  ~4  ^    O 

d  d  d  d  do 


11 


§000 
o  o  >o 


O         >O    O    >O    »O 
00  «M    t^    §    ^ 


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VO    >O 


HARD 
DRAW 


O   O  O  O 

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CM    OO    NO  NO    Tjt 

»H     Tj<    ON  IO     CM 

ro"  CM"  ^<"       -*"  *+ 


« 


sss   ss 


0000  0000  00 

OO>OIO  ONOCON'J'  CMCM 

do'dd  dodo  do 

popo  —  M  »o  -*•  »o\o 


Transmission  Towers 


63 


u 


l- 


iO  so  •*  PN    •*  10  00  iO    O'* 
CN  IO  Os  00    lOCsOOfN 


SO  O        O    —    Os    Os 
PN  O       r~~   -f   10   O 

O     Tf  I-     —      SO     — 


O    O 

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00   O        — 


Os    00        -H    sO    CN 


sO    CN    00 

^^  -i  o 


o    55 

Q2=l 


O    t^    Os         t^    *->    O    fN 

OO    •<*    -+        00    Tj<    Os    iO 


00    t^    -rt* 


10      -H      -H      10 

•^   -H    \O   >O 

CS    «- 1    Os    00 


!       ^t    •«*    ro 
Os    fS   to 


%   $  3 


oooo      o 

so   O   fO   so        O 


oooo      oooo 

OO'-iCvlOs        OvOTj<io 


oooo     o  o 


So     oooo     oooo 
OO         sOfNrt<OO        OCNOOO 


O   Os        00   O   iO 


»—  i  O  Os  OO   t*-  >O  ^ 


Ol  ^^  »^    "^ 


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o    . 


^*    iO    *"^    vO        ^^    f}    CXI    OO        *O    Os   t**»    ^^        PO    OO    ^^    sO 

Os    >O    »— i    t-»         POO'sOPC         OOOsOtO         ^POCNfN 
P^POCOCN       PN   —   —   -H       —   000       OOOO 


O    O    00        O    CN    iO    OO 

O   O   Os        Os   00  t^-   I*- 


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IT)          O    «O 

M*    ^-    f*5         **5    CM 


64 


Transmission  Towers 


CQ 


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i 

i 
£ 


d 
& 


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2 
*o 

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a 


MAX.  LOAD  P 
LIN.  FOOT  PLA 
OF  RESU 


D  PER  LIN. 
HORIZONTA 


IN. 

CAL 


D  P 
V 


s 


II 


ON    OO    IN    NO         i-tfOO-*         NOON 
lOOf^f^  IO    tO    NO    C4  »•*     CN 

NO    «-*    NO    fO         O    00    NO    «O         •*    tO 


t-~  t^  00  >O  NO  O  ^  to 
•n*  OO  ON  ^«  ON  ^>  NO  00 
OO  NO  •<*  Tj<  ts  <N  »-«  O 


t~-  NO  oo  ^  oo  NO  oo 

fO    OO    I-H    fO  (N    t~-     O 

_^                                  OONOlO^  tOtNtS 

O 

ootsoONC  NOIO>OOO  »-i 

s<:s       2^S^  l?«^  ^ 

-iOOO  OOOO  OO 

ON    a    00    00  t-    f^    t^    r-.  NO    >0 

<O(NOO  OOOOI^NO  NOIO 

q  q  q  q  ON  ON  ON  ON  oq  oo 

^  _•  ^  _;  d  d  d  d  do 

OrJtTtCN  NOTfO1^"  fO    «-i 

d  d  o*  d  d  d  d  d  do 

Tl<<NfSto  oor-ooON  NOOO 

NOOOOOt-'  (ONOt^ON  ^    »-i 

OOONOIO  Ttf^cvJ*H.  *~!  '"I 

NOONfOON  ONtOfOOO  O«"» 

t—    O    to    P<1  O^NOON  NOfS 

TJ<fO'-iq  ONOOI^-NO  ^^O 

^  ^  ^  ^  odd  d  d  d 

NOCNOO  *"• '  NO  ON  NO  tO*^ 

**;  ^  "1  ^  t*J(SJ'^^  ^*"1 

d  d  d  d  dodo"  do 

OOOO  OOOO  OO 

00*00  100*0*0  *oo 

lO  O  O  O  lO  to  »O 
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O)C.            OOOO  OOOO 

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SHJ       rf«5^  Urf«- 

(NOOiOON  t^-nrooO  ONO 

NO^H^*CN  iOfN*^r^  NOO 

NOtOOOO  NOlOTj«fO  P^(N 

^^^,q  qqqq  qq 

dddd  dddd  do 

dddd  dddd  do 

888°  -^"^  "^ 


Transmission  Towers 


65 


3 


^  °.  *°> 

to"  to"  ^ 


PC    O    OO    NO        vO    to    OO 
PC   t-    O    r-        <N    00    ON 

to  PC  OO  PC   «— '  OO  ^ 


5  o_  o 
5.  o  o. 


CO    CO    <N    CM 


21, 
IP 


OO  ON  «-H  «N    PC 
PC  PC  ^<  ^«    ^ 


tOt^        OOOOOfN        PCtONO 
— r   -r       ^frtitoto       tototo 


NOcsNOto      t^-^<oo«^      »-«?Ne^i^      OPC 

iOtOTj<PC        to    fN    O    »— i        NOO»-^PC        i--.»-( 
^^OOXOO        t^l^Oto        rJ<Tj<PCP^        *-**-* 


ONOOXt^        OOtoOXto        tOt^tONO        f*5 

,r.     —     i  ~     "-.          OONTt<O          OOtO'-«t^. 


^H    ^    ^H         O    O    O    ON 


o      oO"-<-Hto      «M«^r^ 

PC        t^*    O^    PC    to        ON    PC    ON 
O        O\ONOOr—        NONOtO 


-' 


O   O 
O    »O 


000 
«N    »-«    Ov 

to  PO  to 


0000 
•^H  »-i  fN  fN 
t^  ^  ON  IO 


S 


O   O   O        O   O   O   O 

CS    O     O          Tj«    C^J    00    00 

Ox    to    O        O    O    i—*    O 


Tt<      CS     -^      O 


o  o  o  o     o  o  o 

^1  °°.  ^  °.     ^  °1  ^l 
*o~  TjT  PC"  PC"     «N"  *-*  »-T 


<l™ 


o  to  o  o 

CN  rj«  (N  Tj< 

O>  t-  ^  O 

PC  PO  PO  «N 


NO    IO    IO    00         to    ON    t— 

tO    ON    O    i-"         •<*    01    iO 

PC   O    NO   PC        O   00   NO 


111 


t^    rt<    to        to    iO    to    O 

PC    OO    to         »-H    pvl    PC    f» 


ON   00        00  t^   t- 


0  Ov  0 

00  to  CM 

P><  00  «N 

NO  tO  IO 


0 

Tj< 


00 

O     «N 
>O    Tj« 


§OO        O   O    CN 
IO    O         CN    PC    ^i- 
00    ON    00        «N    to    O 


t^-    NO   to        »O 


o  o  o      **  o  o  o 
to  o  to      *->  o  to 


66  Transmission  Towers 


SAGS 

In  the  following  tables  are  given  sags  at  which  conductors  shall  be 
strung  in  order  that,  when  loaded  with  the  specified  requirement  of 
one-half  inch  of  ice  and  a  wind  load  of  8.0  pounds  per  square  foot  of 
projected  area  at  0  degrees  Fahrenheit,  the  tension  in  the  conductor 
will  not  exceed  the  allowable  value  of  one-half  the  ultimate  strength  of 
the  conductor  as  given  in  preceding  tables.  The  sags  given  in  the 
tables  for  120  degrees  Fahrenheit  are  greater  in  every  case  than  the 
vertical  component  of  the  sags  at  0  degrees  Fahrenheit  under  the 
maximum  wind  and  ice  load. 


Transmission  Towers 


67 


Minimum  Sags  for  Stranded  Hard -Drawn  Bare  Copper  Wires 

No.  4/0  B.  &  S. 


SPAN  IN  FEET 

F. 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

—20 

2 

3 

5 

8 

13 

20 

3.5 

6 

10 

0 

2 

4 

5 

9 

14 

22 

3.5 

6.5 

10.5 

20 

3 

4 

6 

10 

16 

24 

4 

7 

11.5 

40 

3 

4 

6 

11 

18 

27 

4.5 

8 

12 

60 

3 

5 

7 

13 

20 

31 

5 

8.5 

13 

80 

4 

6 

8 

15 

24 

35 

5.5 

9 

13.5 

100 

4 

7 

10 

17 

27 

40 

6 

10 

14.5 

120 

5 

8 

12 

20 

31 

46 

7 

10.5 

15 

No.  3/0  B.  &  S. 


SPAN  IN  FEET 

F. 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

—20 

2 

3 

5 

8 

13 

21 

4 

7 

12 

0 

2 

4 

5 

9 

15 

23 

4 

7.5 

12.5 

20 

3 

4 

6 

10 

17 

25 

4.5 

8.5 

13.5 

40 

3 

4 

6 

12 

19 

29 

5 

9 

14 

60 

3 

5 

7 

13 

22 

33 

6 

9.5 

15 

80 

4 

6 

8 

15 

25 

38 

6.5 

10.5 

15.5 

100 

4 

7 

10 

18 

29 

43 

7 

11 

16 

120 

5 

8 

12 

21 

34 

49 

7.5 

12 

17 

No.  2/0  B.  &  S. 


SPAN  IN  FEET 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

—20 

2 

3 

5 

9 

14 

23 

4.5 

9 

15 

0 

2 

4 

5 

10 

16 

26 

5 

9.5 

15.5 

20 

3 

4 

6 

11 

18 

29 

5.5 

10 

16 

40 

3 

4 

7 

12 

21 

33 

6 

11 

17 

60 

3 

5 

7 

14 

24 

37 

6.5 

11.5 

17.5 

80 

4 

6 

9 

16 

28 

43 

7 

12 

18 

100 

5 

7 

10 

19 

32 

48 

8 

12.5 

18.5 

120 

6 

9 

12 

23 

37 

54 

8.5 

13.5 

19.5 

No.  0  B.  &  S. 


SPAN  IN  FEET 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet  % 

Feet 

—20 

2 

3 

5 

9 

16 

2.5 

5.5 

11.5 

18.5 

0 

2 

4 

5 

10 

18 

2.5 

6.5 

12 

19 

20 

3 

4 

6 

11 

21 

3 

7 

12.5 

19.5 

40 

3 

5 

7 

13 

24 

3.5 

7.5 

13 

20 

60 

3 

5 

8 

15 

27 

4 

8 

14 

20.5 

80 

4 

6 

9 

18 

32 

4.5 

8.5 

14.5 

21.5 

100 

5 

7 

11 

21 

'    37 

5 

9 

15 

22 

120 

6 

9 

13 

25 

42 

5 

9.5 

15.5 

22.5 

68 


Transmission  Towers 


Minimum  Sags  for  Solid  Hard -Drawn  Bare  Copper  Wire 

No.  1  B.  &  S. 


SPAN  IN  FEET 

Temp. 

F. 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

Feet 

—20 

2 

4 

5 

10 

19 

3 

8 

14.5 

23 

0 

3 

4 

6 

11 

22 

3.5 

8.5 

15 

23.5 

20 

3 

4 

6 

13 

25 

4 

9 

16 

24 

40 

3 

5 

7 

15 

30 

4.5 

9.5 

16 

24.5 

60 

4 

6 

8 

18 

34 

5 

10 

17 

25 

80 

4 

7 

10 

21 

39 

5.5 

10.5 

17 

25.5 

100 

5 

8 

12 

25 

44 

6 

11 

18 

26 

120 

6 

10 

16 

30 

49 

6 

11.5 

18 

26.5 

No.  2  B.  &  S. 


SPAN  IN  FEET 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

Feet 

—20 

2 

4 

5 

12 

25 

4 

10.5 

18.5 

29 

0 

3 

4 

6 

14 

29 

4.5 

11 

19 

29.5 

20 

3 

5 

7 

16 

33 

5 

11.5 

19.5 

30 

40 

3 

5 

8 

19 

39 

5.5 

12 

20 

30.5 

60 

4 

6 

10 

23 

43 

6 

12.5 

20.5 

31 

80 

4 

7 

12 

27 

48 

6.5 

13 

21 

31 

100 

5 

9 

14 

31 

53 

7 

13 

21.5 

31.5 

120 

7 

11 

18 

35 

58 

7.5 

13.5 

22 

32 

No.  3  B.  &  S. 


SPAN  IN  FEET 

Temp. 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

—20 

3 

4 

6 

17 

3 

6 

14 

24 

37.5 

0 

3 

4 

7 

20 

3.5 

6.5 

14.5 

24.5 

37.5 

20 

3 

5 

8 

23 

4 

7 

15 

25 

38 

40 

3 

6 

10 

27 

4.5 

7.5 

15 

25 

38 

60 

4 

7 

12 

30 

5 

8 

15.5 

25.5 

38.5 

80 

5 

9 

14 

35 

5.5 

8.5 

10 

26 

39 

100 

6 

11 

17 

39 

5.5 

8.5 

16.5 

26 

39 

120 

8 

14 

22 

44 

6 

9 

16.5 

26.5 

39.5 

No.  4  B.  &  S. 


SPAN  IN  FEET 

Temp. 

F. 

100 

or  Less 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

—20 

3 

4 

8 

25 

5 

9 

18 

31 

46 

0 

3 

5 

9 

29 

5.5 

9 

18.5 

31.5 

46 

20 

3 

6 

11 

33 

6 

9.5 

19 

31.5 

46.5 

40 

4 

7 

13 

38 

6.5 

10 

19 

32 

46.5 

60 

4 

9 

16 

42 

6.5 

10 

19.5 

32.5 

47 

80 

5 

11 

19 

46 

7 

10.5 

19.5 

32.5 

47.5 

100 

7 

13 

23 

50 

•      7.5 

11 

20 

32.5 

47.5 

120 

9 

16 

27 

54 

7.5 

11 

20.5 

33 

48 

Transmission  Towers 


69 


Minimum  Sags  for  Stranded  Bare  Aluminum  Wires 

No.  4/0  B.  &  S. 


SPAN  IN  FEET 

Temp. 

F. 

80 

or  Less 

100 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

—20 

1 

2 

3 

S 

11 

2.5 

5 

11 

19 

29 

0 

1 

2 

3 

6 

15 

3 

5.5 

12 

19.5 

29.5 

20 

2 

3 

5 

8 

21 

3.5 

6 

12.5 

20.5 

30 

40 

2 

4 

7 

11 

27 

4.5 

7 

13 

21 

31 

60 

4 

6 

11 

17 

34 

5 

7.5 

13.5 

21.5 

31.5 

80 

6 

10 

16 

22 

41 

5.5 

8 

14 

22 

32 

100 

10 

14 

20 

27 

46 

6 

8.5 

14.5 

22.5 

33 

120 

13 

18 

25 

32 

52 

6.5 

9 

15 

23 

33.5 

No.  3/0  B.  &  S. 


SPAN  IN  FEET 

Temp. 

F. 

80 

or  Less 

100 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

—20 

1 

2 

3 

5 

12 

3 

5.5 

13 

22 

33.5 

0 

1 

2 

4 

6 

17 

3.5 

6.5 

13.5 

22.5 

34 

20 

2 

3 

5 

8 

24 

4.5 

7 

14 

23 

34.5 

40 

2 

4 

7 

12 

31 

5 

7.5 

14.5 

23.5 

35 

60 

3 

5 

11 

18 

38 

5.5 

8 

15 

24 

35.5 

80 

6 

9 

16 

23 

43 

6 

8.5 

15.5 

24.5 

36 

100 

10 

13 

20 

29 

49 

6.5 

9 

16 

25 

36.5 

120 

13 

17 

25 

33 

54 

7 

9.5 

16.5 

25.5 

37 

No.  2/0  B.  &  S. 


SPAN  IN  FEET 

Temp. 

F 

80 

or  Less 

100 

125 

150 

200 

250 

300 

400 

500 

600 

Inches 

Inches 

Inches 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

—20 

1 

2 

3 

6 

2 

5 

8.5 

16.5 

28 

42 

0 

2 

2 

4 

8 

2.5 

5.5 

9 

17 

28.5 

42.5 

20 

2 

3 

6 

12 

3 

6 

9 

17.5 

29 

43 

40 

2 

4 

9 

18 

3.5 

6.5 

9.5 

18 

29.5 

43 

60 

4 

7 

14 

24 

4 

7 

10 

18.5 

29.5 

43.5 

80 

7 

12 

19 

29 

4.5 

7 

10.5 

19 

30 

44 

100 

10 

16 

24 

33 

5 

7.5 

11 

19.5 

30.5 

44.5 

120 

14 

19 

28 

38 

5.5 

8 

11.5 

20 

31 

44.5 

No.  0  B.  &  S. 


SPAN  IN  FEET 

Temp. 

F.P 

80 

or  Less 

100 

125 

150 

200 

250 

300 

400 

500 

Inches 

Inches 

Inches 

Inches 

Feet 

Feel 

Feet 

Feet 

Feet 

—20 

1 

2 

4 

9 

3.5 

7 

10.5 

21 

36.5 

0 

2 

3 

6 

14 

4 

7 

11 

21.5 

36.5 

20 

2 

4 

8 

20 

4.5 

7.5 

11.5 

22 

37 

40 

3 

6 

13 

26 

5 

8 

12 

22 

37 

60 

5 

10 

18 

31 

5 

8.5 

12 

22.5 

37.5 

80 

8 

14 

23 

35 

5.5 

8.5 

12.5 

23 

38 

100 

12 

18 

27 

39 

6 

9 

13 

23 

38 

120 

15 

21 

31 

43 

6 

9.5 

13.5 

23.5 

-38.5 

70  Transmission  Towers 

GALVANIZING  IRON  AND  STEEL 

We  recommend  the  specifications  adopted  by  the  National  Electric 
Light  Association,  which  are  as  follows: 

These  specifications  give  in  detail  the  test  to  be  applied  to  galva- 
nized material.   All  specimens  shall  be  capable  of  withstanding  these 
tests. 
a — Coating 

The  galvanizing  shall  consist  of  a  continuous  coating  of  pure  zinc 
of  uniform  thickness,  and  so  applied  that  it  adheres  firmly  to  the  sur- 
face of  the  iron  or  steel.     The  finished  product  shall  be  smooth. 
b — Cleaning 

The  samples  shall  be  cleaned  before  testing,  first  with  carbona, 
benzine  or  turpentine,  and  cotton  waste  (not  with  a  brush),  and  then 
thoroughly  rinsed  in  clean  water  and  wiped  dry  with  clean  cotton 
waste. 

The  samples  shall  be  clean  and  dry  before  each  immersion  in  the 
solution. 
c — Solution 

The  standard  solution  of  copper  sulphate  shall  consist  of  commercial 
copper  sulphate  crystals  dissolved  in  cold  water,  about  in  the  propor- 
tion of  36  parts,  by  weight,  of  crystals  to  100  parts,  by  weight,  of  water. 
The  solution  shall  be  neutralized  by  the  addition  of  an  excess  of 
chemically  pure  cupric  oxide  (Cu  O).  The  presence  of  an  excess  of 
cupric  oxide  will  be  shown  by  the  sediment  of  this  reagent  at  the  bot- 
tom of  the  containing  vessel. 

The  neutralized  solution  shall  be  filtered  before  using  by  passing 
through  filter  paper.  The  filtered  solution  shall  have  a  specific 
gravity  of  1.186  at  65  degrees  Fahrenheit  (reading  the  scale  at  the  level 
of  the  solution)  at  the  beginning  of  each  test.  In  case  the  filtered 
solution  is  high  in  specific  gravity,  clean  water  shall  be  added  to  re- 
duce the  specific  gravity  to  1.186  at  65  degrees  F.  In  case  the  filtered 
solution  is  low  in  specific  gravity,  filtered  solution  of  a  higher  specific 
gravity  shall  be  added  to  make  the  specific  gravity  1.186  at  65  degrees 
Fahrenheit. 

As  soon  as  the  stronger  solution  is  taken  from  the  vessel  containing 
the  unfiltered  neutralized  stock  solution,  additional  crystals  and 
water  must  be  added  to  the  stock  solution.  An  excess  of  cupric  oxide 
shall  always  be  kept  in  the  unfiltered  stock  solution. 


Transmission  Towers  71 

d — Quantity  of  Solution 

Wire  samples  shall  be  tested  in  a  glass  jar  of  at  least  two  (2)  inches 
inside  diameter.  The  jar  without  the  wire  samples  shall  be  filled  with 
standard  solution  to  a  depth  of  at  least  four  (4)  inches.  Hardware 
samples  shall  be  tested  in  a  glass  or  earthenware  jar  containing  at 
least  one-half  (J/£)  pint  of  standard  solution  for  each  hardware  sample. 

Solution  shall  not  be  used  for  more  than  one  series  of  four  immer- 
sions. 

e — Samples 

Not  more  than  seven  wires  shall  be  simultaneously  immersed,  and 
not  more  than  one  sample  of  galvanized  material,  other  than  wire,  shall 
be  immersed  in  the  specified  quantity  of  solution. 

The  samples  shall  not  be  grouped  or  twisted  together,  but  shall  be 
well  separated  so  as  to  permit  the  action  of  the  solution  to  be  uniform 
upon  all  immersed  portions  of  the  samples. 

f— Test 

Clean  and  dry  samples  shall  be  immersed  in  the  required  quantity  of 
standard  solution  in  accordance  with  the  following  cycle  of  immersions. 

The  temperature  of  the  solution  shall  be  maintained  between  62 
and  68  degrees  Fahrenheit  at  all  times  during  the  following  test. 

First — Immerse  for  one  minute,  wash  and  wipe  dry. 

Second — Immerse  for  one  minute,  wash  and  wipe  dry. 

Third — Immerse  for  one  minute,  wash  and  wipe  dry. 

Fourth — Immerse  for  one  minute,  wash  and  wipe  dry. 

After  each  immersion  the  samples  shall  be  immediately  washed  in 
clean  water  having  a  temperature  between  62  and  68  degrees  Fahren- 
heit, and  wiped  dry  with  cotton  waste. 

In  the  case  of  No.  14  galvanized  iron  or  steel  wire,  the  time  of  the 
fourth  immersion  shall  be  reduced  to  one-half  minute. 

g— Rejection 

If  after  the  test  described  in  Section  "f"  there  should  be  a  bright 
metallic  copper  deposit  upon  the  samples,  the  lot  represented  by  the 
samples  shall  be  rejected. 

Copper  deposits  on  zinc  or  within  one  inch  of  the  cut  end  shall  not 
be  considered  causes  for  rejection. 

In  the  case  of  a  failure  of  only  one  wire  in  a  group  of  seven  wires 
immersed  together,  or  if  there  is  a  reasonable  doubt  as  to  the  copper 
deposit,  two  check  tests  shall  be  made  on  these  seven  wires,  and  the 
lot  reported  in  accordance  with  the  majority  of  the  set  of  tests. 


72 


Transmission  Towers 


USEFUL  DATA 


Given,  ax2  +  bx  -f  c  =  0;  X 


-b  =fe  V  b2  —  4  ac 
2a 


e  =  Base  of  Napierian  Logarithms  =  2.7182818285 


Log]0  C  =  0.4342944819 


(ev 


V^ 


V3 


+ 


^ 

V7 


4- 


V8 


+ 


+ 


V9 


+ 


V5 

IE 

One  inch  =  2.540005  centimeters 
One  centimeter  =  0.3937  inches 
One  foot  =  0.3048006  meter 
One  meter  =  3.2808333  feet 
One  pound  (avoirdupois)  =  0.45359  kilograms 
One  pound  per  foot  =  1.488161  kilograms  per  meter. 
One  pound  per  square  inch  =  0.0703067  kilograms  per  square  centi- 
meter 

One  inch-pound  =  1.152127  kilogram-centimeters 
One  kilogram  per  meter  =  0.67197  pounds  per  foot 
One  kilogram  per  square  centimeter  =  14.2234  pounds  per  square  inch 
One  kilogram-centimeter  =  0.86796  inch-pounds 


Trigonometrical  Formulae 


Radius,  1  =  sin2  A  -f  cos2  A 

=  sin  A  cosec  A  =  cos  A  sec  A  =  tan  A  cot  A 

cos  A  1  .  ,        *       ^  / 


! 

--  cotan  A—      —  *j      sine 

rt  T 

cot  A 

A      sin  A 

cosec  A 

K 

.-^^ 

X 

\ 

ver. 
•in  A 

/__     Cosine 

Tangent 
I 

5  Cotangent 
-l_.i    Secant 
Cnsprant 

r                 cin    A   rot    A          \/  1        cin2    A 

tan  A 
.      sin  A 

sec  A 

=  =sin  A  sec  A 
cot  A 

f       AqkleA    j~~* 

A  - 
cos  A 

»      cos  A 

sin  A 
A_  tanA 

~  tan  A 
1 

*  radius  -i  —  J 

sin  A 
A      cotA 

cos  A 

1 

Transmission  Towers 
NATURAL  TRIGONOMETRIC  FUNCTIONS 


73 


Degrees 

Sines 

Cosines 

Tangents 

Cotangents 

Secants 

Cosecants 

Degrees 

0 
1 
2 
3 

0.00000 
0.01745 
0.03490 
0.05234 

1.00000 
0.99985 
0.99939 
0.99863 

0.00000 
0.01746 
0.03492 
0.05241 

57.28996 
28.63625 
19.08114 

1.00000 
1.00015 
1.00061 
1.00137 

57.29869 
28.65371 
19.10732 

90 
89 
88 
87 

4 
5 
6 
7 

0.06976 
0.08716 
0.10453 
0.12187 

0.99756 
0.99619 
0.99452 
0.99255 

0.06993 
0.08749 
0.10510 
0.12278 

14.30067 
11.43005 
9.51436 
8.14435 

1.00244 
1.00382 
1.00551 
1.00751 

14.33559 
11.47371 
9.56677 
8.20551 

86 
85 
84 
83 

8 
9 
10 
11 

0.13917 
0.15643 
0.17365 
0.19081 

0.99027 
0.98769 
0.98481 
0.98163 

0.14054 
0.15838 
0.17633 
0.19438 

7.11537 
6.31375 
5.67128 
5.14455 

1.00983 
.01247 
.01543 
.01872 

7.18530 
6.39245 
5.75877 
5.24084 

82 
81 
80 
79 

12 
13 
14 
15 

0.20791 
0.22495 
0.24192 
0.25882 

0.97815 
0.97437 
0.97030 
0.96593 

0.21256 
0.23087 
0.24933 
0.26795 

4.70463 
4.33148 
4.01078 
3.73205 

.02234 
.02630 
.03061 
1.03528 

4.80973 
4.44541 
4.13357 
3.86370 

78 
77 
76 

75 

16 
17 
18 
19 

0.27564 
0.29237 
0.30902 
0.32557 

0.96126 
0.95630 
0.95106 
0.94552 

0.28675 
0.30573 
0.32492 
0.34433 

3.48741 
3.27085 
3.07768 
2.90421 

1.04030 
1.04569 
1.05146 
1.05762 

3.62796 
3.42030 
3.23607 
3.07155 

74 
73 
72 
71 

20 
21 
22 
23 

0.34202 
0.35837 
0.37461 
0.39073 

0.93969 
0.93358 
0.92718 
0.92050 

0.36397 
0.38386 
0.40403 
0.42447 

2.74748 
2.60509 
2.47509 
2.35585 

1.06418 
1.07115 
1.07853 
1.08636 

2.92380 
2.79043 
2.66947 
2.55930 

70 
69 
68 
67 

24 
25 
26 

27 

0.40674 
0.42262 
0.43837 
0.45399 

0.91355 
0.90631 
0.89879 
0.89101 

0.44523 
0.46631 
0.48773 
0.50953 

2.24604 
2.14451 
2.05030 
1.96261 

1.09464 
1.10338 
1.11260 
1.12233 

2.45859 
2.36620 
2.28117 
2.20269 

66 
65 
64 
63 

28 
29 
30 
31 

0.46947 
0.48481 
0.50000 
0.51504 

0.88295 
0.87462 
0.86603 
0.85717 

0.53171 
0.55431 
0.57735 
0.60086 

1.88073 
1.80405 
1.73205 
1.66428 

1.13257 
1.14335 
1.15470 
1.16663 

2.13005 
2.06267 
2.00000 
1.94160 

62 
61 
60 
59 

32 
33 
34 
35 

0.52992 
0.54464 
0.55919 
0.57358 

0.84805 
0.83867 
0.82904 
0.81915 

0.62487 
0.64941 
0.67451 
0.70021 

1.60033 
1.53987 
1.48256 
1.42815 

1.17918 
1.19236 
1.20622 
1.22077 

1.88708 
1.83608 
1.78829 
1.74345 

58 
57 
56 
55 

36 
37 
38 
39 

0.58779 
0.60182 
0.61566 
0.62932 

0.80902 
0.79864 
0.78801 
0.77715 

0.72654 
0.75355 
0.78129 
0.80978 

1.37638 
1.32704 
1.27994 
1.23490 

1.23607 
1.25214 
1.26902 
1.28676 

.70130 
.66164 
1.62427 
.58902 

54 
53 
52 
51 

40 
41 
42 
43 

0.64279 
0.65606 
0.66913 
0.68200 

0.76604 
0.75471 
0.74314 
0.73135 

0.83910 
0.86929 
0.90040 
0.93252* 

1.19175 
1.15037 
1.11061 
1.07237 

1.30541 
1.32501 
1.34563 
1.36733 

.55572 
.52425 
.49448 
.46628 

50 
49 
48 
47 

44 

45 

0.69466 
0.70711 

0.71934 
0.70711 

0.96569 
1.00000 

1.03553 
1.00000 

1.39016 
1.41421 

1.43956 
1.41421 

46 

45 

Degrees 

Cosines 

Sines 

Cotangents 

Tangents 

Cosecants 

Secants 

Degrees 

74  Transmission  Towers 

Properties  of  the  Circle 

Circumference  of  Circle  of  Diameter  1  =  -  =  3.14159265 
Circumference  of  Circle  =  2  *  r 
Diameter  of  Circle  =  Circumference  X  0.31831 
Diameter  of  Circle  of  equal  periphery  as 

square  =  side  X  1.27324 

Side  of  Square  of  equal  periphery  as  circle          =  diameter  X  0.78540 
Diameter  of  Circle  circumscribed  about  square  =  side  X  1.41421 

Side  of  Square  inscribed  in  circle  =  diameter  X  0.70711 


Arc»       a  =     TSTT  =  0.017453  r  A 

loU 


4b2  +  c2  4  02 

Radius  r  =  —  T-T  —    Diameter,  d 


, 
80  40 


Chord,  c  =  2V  2br  —  b2  =  2  r  sin  y 

Rise,      b  =  r—Y2  V  4  r2  —  c2  =  £  tan  ~-  =  2  r  sin2  4 

24  4 


Rise,      6  =  r '+  y  —  V  r2  —  ^c2.     ^  =  0  —  r  +  V^2  —  ^2 


^  =  V  r2  —  (r  +  3;  —  0)2 

TT  =  3. 14159265,  log  =  0.4971499 

^  =  0.3183099,  log  =7.5028501 
7T2  =  9.8696044,  log  =  0.9942997 
^  =  0.1013212,  log  =7.0057003 
=  1.7724539,  log  =  0.2485749 
=  0.5641896,  log  =7.7514251 


—  =  0.0174533,  log  =  2.2418774 

loU 

1  80 

—  =  57.2957795,  log  =  1.7581226 


Transmission  Towers  75 

Pyramid  and  Cone 

Volume  of  any  Pyramid  or  Cone  whether  regular  or  irregular  equals 
product  of  area  of  base  by  one-third  perpendicular  height,  or 

V  =  iBh 
in  which 

V  =  Volume 

B  =  Area  of  Base 

h   =  Perpendicular  height 


Volume  of  Frustrum  of  any  Pyramid  or  Cone  with  parallel  ends 
equals  sum  of  areas  of  base  and  top  plus  square  root  of  their  products, 
all  multiplied  by  one-third  the  perpendicular  height  or  distance 
between  the  two  parallel  ends,  or 

V  =  i  h  (B  +  \/Bb  +  b) 
in  which 

V  =  volume 

h   =  perpendicular  distance  between  parallel  ends 

B  =  area  of  base 

b   ==  area  of  top 


76 


Transmission  Towers 


c? 


Ellipse 

Area  =  *  ab 

Center  of  Gravity  of  part  mnc  is  at  point  G 

cGl  =  !     a  •  3  =  0.4244  •  a  =  abt.  H  a 
cGn  =  G'G  =  !  •  b  •  -  =  0.4244  •  b  =  abt. 


Parabola 

4  Area  =  |  sh 

\jh       Center  of  Gravity  at  point  G 


Hft|bd 

L-W—i— tt_. 


Semi-Parabola  —  abd  or  cbd 

Center  of  Gravity  at  Point  G1 

dG  =|h 

GG1  =|-W 

For  the  area  included  between  the  semi-para- 
bola  abd  and  its  enclosing  rectangle  aebd,  or 
between  the  semi-parabola  cbd  and  its  en- 
closing  rectangle  cfbd,  the  center  of  gravity 
is  at  the  point  m. 


km=  —  w 
4 


Circular  Quadrant 

Center  of  Gravity  at  point  G 

V~2 


CG  =  iRad.  X 


Rad.  0.6002 


i 


CX  =  XG  =  J  Rad.  X  £  =  Rad    X  0.4244  or  abt. 
Rad.  X 


Transmission  Towers 


77 


Fig.  B— Towers  for  Double  Circuit  130,000  Volt  Line 


78 


Transmission  Towers 


Fig.  C — Method  of  Erecting  Towers  from  Prone  Position 


Transmission  Towers 


79 


Fig.  D — Method  of  Erecting  Flexible  A  Frames  from  Prone  Position 


80 


Transmission  Towers 


I     A 


Fig.  E— Method  of  Erecting  Towers  in  Position 


Transmission  Towers 


81 


Fiji.  F— Double  Circuit  Towers,  for  66,000  Volt  Line 


82 


Transmission  Towers 


ft 


Fig.  G— Special  Strain  Tower,  for  Double  Circuit  110,000  Volt  Line 


Transmission  Towers 


83 


Fig.  H— Transposition  Tower,  for  Double  Circuit  130,000  Volt  Line 


84 


Transmission  Towers 


Fig.  I— Railroad  Crossing  Poles,  for  6,600  Volt  Line 


Transmission  Towers 


85 


Fig.  J— Flexible  A  Frame,  for  Double  Circuit  66,000  Volt  Line 


86 


Transmission  Towers 


Fig.  K— Flexible  A  Frame,  for  Single  Circuit  66,000  Volt  Line 


Transmission  Towers 


87 


L — Poles,  for  Double  Circuit  6,600  Volt  Line 


INDEX 


Anchor  Towers 

Anchorage  Designs 50,  51 

Angle  Towers 45 


B 


Bolt  Values. 


.  44 


Catenary 16 

Comparison  of  Parabola  and .    . 

Diagram 15 

Elastic 19 

Circle,  Properties  of 

Conductors,  Spacing  of 

Cone,  Volume  of 75 


Dead  End  Towers. 


.   49 


Ellipse ' 76 

Erection 55,78,79,80 

F 

Factor  of  Safety 42 

Flexible  A  Frames,  Illustration  .   85,  86 
Use  of..  .   4 


Galvanizing 41,  70-71 

I 

Ice    and    Wind    Loads,    Standard 
Practice  for 14 

L 

Loads,  Kinds  of 5-6 

Specific 45 

Standard  Practice  for  Wind  and 
Ice 14 

P 

Parabola 76 

Comparison  of  Catenary  and ....    25 

Diagram 20,22,23,27,30 

Parabolic  Arc 23 

Semi 76 

Poles,  Illustration 84,  87 

Railroad  Crossing,  Illustration ...   84 
Use  of. 4 

Pressure  and  Wind  Velocity,  Rela- 
tion between 12,  13 

Pyramid,  Volume  of 75 

0 

Quadrant,  Circular 76 

S 

Sag  Calculations,  Thomas' 33 

Curves  for 34-35 

Relation  Between  Stress,   Tem- 
perature and 31 

Tables..  .   66-69 


S 


Spacing 56 

Spans,  Reactions  for,  on  Inclines.  .  .   27 
Stringing    Wires    in,    on    Steep 

Grades 29 

Specifications  for  Designs 42 

Stress     Calculations,     Thomas' 

Curves  for 34-35 

Relation  Between  Temperature, 

Sag  and 31 

Unit..  .  43 


Temperature,     Relation     Between 
Stress,  Sag  and 31 

Towers,  Anchor 48 

Anchorage  Designs 50 

Angle 45 

Dead  End 49 

Erection 55,  78,  79,  80 

Factor  of  Safety 42 

Installations 2,  77-87 

Permanent 41 

Regular  Line 48 

Rigid,  Use  of 

Spacing  of 37,  56 

Special 46 

Specifications  for  Designs 42 

Standard 48 

Strain,  Illustration  of 82 

Temporary 41 

Thickness  of  Materials  for 41 

Transposition,  Illustration  of. ...   83 

Trigonometrical  Formulae 72 

Functions 73 


U 


Useful  Data. 


72-76 


W 


Wind    and    Ice    Loads,    Standard 
Practice  for 14 

Pressure  on  Plane  Surfaces 7 

On  Wires .   8 

Velocities,   Comparison   of   Indi- 
cated and  Actual 11 

Velocity  and   Pressure,  Relation 

Between 12,  13 

Wires,  Curves  Assumed  by 15 

Loadings  Recommended  for 59 

Materials,  Properties  of 59-65 

Stringing,    in    Spans    on    Steep 
Grades 29 

Tension    in,    Diagram   of   Com- 
ponents of 47 

Values  Used  for  Plotting  Curves 
for 36 

Wind  Pressures  on 8 


89 


Memoranda 


Memoranda 


Memoranda 


Memoranda 


Memoranda 


Memoranda 


PRODUCTS  OF 
THE  BLAW-KNOX  COMPANY 


FABRICATED  STEEL 

Fabricated  steel,  one  of  the  principal  products  of  Blaw-Knox  Company,  includes 
mill  buildings,  manufacturing  plants,  bridges,  crane  runways,  trusses  and  other  con- 
struction of  a  highly  fabricated  nature. 

A  corps  of  highly  trained  engineers  is  maintained  for  consulting  and  designing 
services. 

TRANSMISSION  TOWERS 

Four  legged  straight  line  or  suspension  towers,  anchor  and  dead  end  towers,  latticed 
and  channel  A-frames,  river  crossing  towers,  outdoor  sub-stations,  switching  stations, 
signal  towers,  steel  poles,  derrick  towers. 

We  specialize  in  the  design  and  fabrication  of  high  tension  transmission  lines. 

PLATE  WORK 

Riveted,  pressed  and  welded  steel  plate  products  of  every  description,  including: 
accumulators,  agitators,  water  boshes,  annealing  boxes,  containers,  digesters,  filters, 
flumes,  gear  guards,  kettles,  ladles,  pans,  penstocks,  air  receivers,  stacks,  standpipes, 
miscellaneous  tanks,  miscellaneous  blast  furnace  work,  etc. 

BLAW  BUCKETS 

Clamshell  buckets  and  automatic  cableway  plants  for  digging  and  rehandling 
earth,  sand,  gravel,  coal,  ore,  limestone,  tin  scrap,  slag,  cinders,  fertilizers,  rock 
products,  etc. 

For  installation  on  derricks,  overhead  and  locomotive  cranes,  monorails,  dredges, 
steam  shovels,  ditchers,  cableways,  ships  for  handling  cargo  and  coal,  etc. 

BLAWFORMS 

Steel  forms  for  every  type  of  concrete  construction:  aqueducts,  bridges,  cisterns, 
columns,  culverts,  curbs  and  gutters,  dams,  factories,  floors,  foundations,  houses, 
locks,  manholes,  piers,  pipe,  reservoirs,  roads,  sewers,  shafts,  sidewalks,  subways, 
tanks,  tunnels,  viaducts,  retaining  walls,  warehouses,  etc. 

FURNACE  APPLIANCES 

Knox  patented  water  cooled  doors,  door  frames,  front  and  back  wall  coolers,  ports, 
bulkheads,  reversing  valves,  etc.,  for  Open  Hearth.  Glass  and  Copper  Regenerative 
Furnaces;  water-cooled  standings,  boshes  and  shields  for  Sheet  and  Tin  Mills. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 

AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


MAR    2  1946 


LD  21-100/n-7,'40(6936s) 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


